Table of contents

Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in four-dimensional scalar theories, 2n derivatives of the fields, n>1, do not appear before the n th loop. A new kind of expansion can be defined to treat functions of the fields (but not of their derivatives) non-perturbatively. I study the conditions under which these theories can be consistently renormalized with a reduced, eventually finite, set of independent couplings. I find that in common models the number of couplings sporadically grows together with the order of the expansion, but the growth is slow and a reasonably small number of couplings is sufficient to make predictions up to very high orders. Various examples are solved explicitly at one and two loops.

A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d+1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.

The R⁴-type corrections to ten and eleven dimensional supergravity required by string and M-theory imply corrections to supersymmetric supergravity compactifications on manifolds of special holonomy, which deform the metric away from the original holonomy. Nevertheless, in many such cases, including Calabi-Yau compactifications of string theory and G₂-compactifications of M-theory, it has been shown that the deformation preserves supersymmetry because of associated corrections to the supersymmetry transformation rules, Here, we consider Spin(7) compactifications in string theory and M-theory, and a class of non-compact SU(5) backgrounds in M-theory. Supersymmetry survives in all these cases too, despite the fact that the original special holonomy is perturbed into general holonomy in each case.

We derive Bogomolny-type equations for the abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary conditions have to be handled in noncommutative space and discuss how vortex solutions are constructed. We also consider the extension to an U(2) × U(1) model, a simplified prototype of the noncommutative standard model.

There is a general scaling argument that shows that the entropy of a small black hole, representing a half-BPS excitation of an elementary heterotic string in any dimension, agrees with the statistical entropy up to an overall numerical factor. We propose that for suitable choice of field variables the near horizon geometry of the black hole in D space-time dimensions takes the form of AdS₂ × S^D−2 and demonstrate how this ansatz can be used to calculate the numerical factor in the expression for the black hole entropy if we know the higher derivative corrections to the action. We illustrate this by computing the entropy of these black holes in a theory where we modify the supergravity action by adding the Gauss-Bonnet term. The black hole entropy computed this way is finite and has the right dependence on the charges in accordance with the general scaling argument, but the overall numerical factor does not agree with that computed from the statistical entropy except for D = 4 and D = 5. This is not surprising in view of the fact that we do not use a fully supersymmetric action in our analysis; however this analysis demonstrates that higher derivative corrections are capable of stretching the horizon of a small black hole in arbitrary dimensions.

We present new exact three-dimensional black-string backgrounds, which contain both NS-NS and electromagnetic fields, and generalize the BTZ black holes and the black string studied by Horne and Horowitz. They are obtained as deformations of the SL(2,) WZW model. Black holes resulting from purely continuous deformations possess true curvature singularities. When discrete identifications are introduced, extra chronological singularities appear, which under certain circumstances turn out to be naked. The backgrounds at hand appear in the moduli space of the SL(2,) WZW model. Hence, they provide exact string backgrounds and allow for a more algebraical (CFT) description. This makes possible the determination of the spectrum of primaries.

IR divergences of a non-commutative U(1) Maxwell theory are discussed at the one-loop level using an interpolating gauge to show that quadratic IR divergences are independent not only from a covariant gauge fixing but also independent from an axial gauge fixing.

We study the construction of D-brane boundary states in the pure spinor formalism for the quantisation of the superstring. This is achieved both via a direct analysis of the definition of D-brane boundary states in the pure spinor conformal field theory, as well as via comparison between standard RNS and pure spinor descriptions of the superstring. Regarding the map between RNS and pure spinor formulations of the superstring, we shed new light on the tree level zero mode saturation rule. Within the pure spinor formalism we propose an explicit expression for the D-brane boundary state in a flat spacetime background. While the non-zero mode sector mostly follows from a simple understanding of the pure spinor conformal field theory, the zero mode sector requires a deeper analysis which is one of the main points in this work. With the construction of the boundary states at hand, we give a prescription for calculating scattering amplitudes in the presence of a D-brane. Finally, we also briefly discuss the coupling to the world-volume gauge field and show that the D-brane low-energy effective action is correctly reproduced.

A detailed analysis of a Stueckelberg extension of the electro-weak gauge group with an extra abelian U(1)_X factor is presented for the Standard Model as well as for the MSSM. The extra gauge boson gets massive through a Stueckelberg type coupling to a pseudo-scalar, instead of a Higgs effect. This new massive neutral gauge boson Z' has vector and axial vector couplings uniquely different from those of conventional extra abelian gauge bosons, such as appear e.g. in GUT models. The extended MSSM furthermore contains two extra neutralinos and one extra neutral CP-even scalar, the latter with a mass larger than that of the Z'. One interesting scenario that emerges is an LSP that is dominantly composed out of the new neutralinos, leading to a possible new superweak candidate for dark matter. We investigate signatures of the Stueckelberg extension at a linear collider and discuss techniques for the detection of the expected sharp Z' resonance. It turns out that the substantially modified forward-backward asymmetry around the Z' pole provides an important signal. Furthermore, we also elaborate on generalizations of the minimal Stueckelberg extension to an arbitrary number of extra U(1) gauge factors.

We consider multi-parton collinear limits of QCD amplitudes at tree level. Using the MHV formalism we specify the underlying analytic structure of the resulting multi-collinear splitting functions. We derive general results for these splitting functions that are valid for specific numbers of negative helicity partons and an arbitrary number of positive helicity partons (or vice versa).

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of = (2,2) nonlinear sigma-models. The most direct relation is obtained at the = (1,1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of = (2,2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kähler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.

We demonstrate that flux compactifications of type IIA string theory can classically stabilize all geometric moduli. For a particular orientifold background, we explicitly construct an infinite family of supersymmetric vacua with all moduli stabilized at arbitrarily large volume, weak coupling, and small negative cosmological constant. We obtain these solutions from both ten-dimensional and four-dimensional perspectives. For more general backgrounds, we study the equations for supersymmetric vacua coming from the effective superpotential and show that all geometric moduli can be stabilized by fluxes. We comment on the resulting picture of statistics on the landscape of vacua.

In supersymmetric models with gravity-mediated SUSY breaking, universality of soft SUSY breaking sfermion masses m₀ is motivated by the need to suppress unwanted flavor changing processes. The same motivation, however, does not apply to soft breaking Higgs masses, which may in general have independent masses from matter scalars at the GUT scale. We explore phenomenological implications of both the one-parameter and two-parameter non-universal Higgs mass models (NUHM1 and NUHM2), and examine the parameter ranges compatible with Ω_CDMh², BF(b→sγ) and (g−2)_μ constraints. We have demonstrated that in contrast to the mSUGRA model, in both NUHM1 and NUHM2 models, the dark matter A-annihilation funnel can be reached at low values of tan β, while the higgsino dark matter annihilation regions can be reached for low values of m₀. We show that there may be observable rates for indirect and direct detection of neutralino cold dark matter in phenomenologically aceptable ranges of parameter space. We also examine implications of the NUHM models for the Fermilab Tevatron, the CERN LHC and a (s)^1/2 = 0.5−1 TeV e⁺e⁻ linear collider. Novel possibilities include: very light _R, _R squark and _L slepton masses as well as light charginos and neutralinos and H, A and H^± Higgs bosons.

We revisit bosonization of non-relativistic fermions in one space dimension. Our motivation is the recent work on bubbling half-BPS geometries by Lin, Lunin and Maldacena [13]. After reviewing earlier work on exact bosonization in terms of a noncommutative theory, we derive an action for the collective field which lives on the droplet boundaries in the classical limit. Our action is manifestly invariant under time-dependent reparametrizations of the boundary. We show that, in an appropriate gauge, the classical collective field equations imply that each point on the boundary satisfies Hamilton's equations for a classical particle in the appropriate potential. For the harmonic oscillator potential, a straightforward quantization of this action can be carried out exactly for any boundary profile. For a finite number of fermions, the quantum collective field theory does not reproduce the results of the exact noncommutative bosonization, while the latter are in complete agreement with the results computed directly in the fermi theory.

In a previous paper we had proposed a specific route to relating the entropy of two charge black holes to the degeneracy of elementary string states in N=4 supersymmetric heterotic string theory in four dimensions. For toroidal compactification this proposal works correctly to all orders in a power series expansion in inverse charges provided we take into account the corrections to the black hole entropy formula due to holomorphic anomaly. In this paper we demonstrate that similar agreement holds also for other N=4 supersymmetric heterotic string compactifications.

Important corrections to BFKL evolution are obtained from non-leading contributions and from non-linear effects due to unitarisation or saturation. It has been difficult to estimate the relative importance of these effects, as NLO effects are most easily accounted for in momentum space while unitarisation and saturation are easier in transverse coordinate space. An essential component of the NLO contributions is due to energy conservation effects, and in this paper we present a model for implementing such effects together with saturation in Mueller's dipole evolution formalism. We find that energy conservation severely dampens the small-x rise of the gluon density and, as a consequence, the onset of saturation is delayed. Using a simple model for the proton we obtain a reasonable qualitative description of the x-dependence of \ftwo at low Q² as measured at HERA even without saturation effects. We also give qualitative descriptions of the energy dependence of the cross section for γ^⋆γ^⋆ and γ^⋆−nucleus scattering.

We show that the conifold and deformed-conifold warped compactifications of the ten-dimensional type-IIB supergravity, including the Klebanov-Strassler solution, are dynamically unstable in the moduli sector representing the scale of a Calabi-Yau space, although it can be practically stable for a quite long time in a region with a large warp factor. This instability is associated with complete supersymmetry breaking except for a special case and produces significant time-dependence in the structure of the four-dimensional base spacetime as well as of the internal space.

It is shown that knotted topological strings appear at the symmetric phase of Higgs field in the context of generalized Yang-Mills Chern-Simons Higgs model. The equation of motion of the knotted strings coupled with the Kalb-Ramond field is obtained. Based on the equation of motion, we found that there is a topological constrain on the coupling term between Maxwell field and the covariant derivative of Kalb-Ramond field, the topological number of this coupling is the topological number of the abelian Chern-Simons action on the knotted topological strings.

A class of covariant gauges allowing one to interpolate between the Landau, the maximal abelian, the linear covariant and the Curci-Ferrari gauges is discussed. Multiplicative renormalizability is proven to all orders by means of algebraic renormalization. All one-loop anomalous dimensions of the fields and gauge parameters are explicitly evaluated in the scheme.

Experiments strongly suggest that the flavour mixing responsible for the atmospheric neutrino anomaly is very close to being maximal. Thus, it is of great theoretical as well as experimental importance to measure any possible deviation from maximality. In this context, we reexamine the effects of matter interactions in long baseline neutrino oscillation experiments. Contrary to popular belief, the muon neutrino survival probability is shown to be quite sensitive to matter effects. Moreover, for moderately long baselines, the difference between the survival probilities for ν_μand _μis shown to be large and sensitive to the deviation of |U_μ3| from maximality. Performing a realistic analysis, we demonstrate that a muon-storage ring ν-source alongwith an iron calorimeter detector can measure such deviations. (Contrary to recent claims, this is not so for the NuMI-MINOS experiment.) We also discuss the possible correlation in measuring U_μ3and U_e3in such experiment.

Current data on CP violation in B_d→η'K_S and B_d→ϕK_S, taken literally, suggest new physics contributions in b→s transitions. Despite a claim to the contrary, we point out that right-handed operators with a single weak phase can account for both deviations thanks to the two-fold ambiguity in the extraction of the weak phase from the corresponding CP-asymmetry. This observation is welcome since large mixing in the right-handed sector is favored by many GUT models and frameworks which address the flavor puzzle. There are also interesting correlations with the B_s system which provide a way to test this scenario in the near future.

All consistent interactions in five spacetime dimensions that can be added to a free BF-type model involving one scalar field, two types of one-forms, two sorts of two-forms, and one three-form are investigated by means of deforming the solution to the master equation with the help of specific cohomological techniques. The couplings are obtained on the grounds of smoothness, locality, (background) Lorentz invariance, Poincaré invariance, and the preservation of the number of derivatives on each field.

We extend the methods of Spradlin and Volovich to compute the partition function for a conformally-invariant gauge theory on × S³ in which the dilatation operator is represented by a spin-chain hamiltonian acting on pairs of states, not necessarily nearest neighbors. A specific application of this is the two-loop dilatation operator of the planar SU(2) subsector of the = 4 SU(N) super Yang-Mills theory in the large-N limit. We compute the partition function and Hagedorn temperature for this sector to second order in the gauge coupling. The Hagedorn temperature is to be interpreted as giving the exponentially-rising portion of the density of states of the SU(2) sector, which may be a signal of stringy behavior in the dual theory.

We extend the algorithm for matching fixed-order tree-level matrix element generators with the Dipole Cascade Model in Ariadne to apply to processes with incoming hadrons. We test the algoritm on for the process W+n jets at the Tevatron, and find that the results are fairly insensitive to the cutoff used to regularize the soft and collinear divergencies in the tree-level matrix elements. We also investigate a few observables to check the sensitivity to the matrix element correction.

We argue that topological matrix models (matrix models of the Kontsevich type) are examples of exact open/closed duality. The duality works at finite N and for generic 't Hooft couplings. We consider in detail the paradigm of the Kontsevich matrix integral for two-dimensional topological gravity. We demonstrate that the Kontsevich model arises by topological localization of cubic open string field theory on N stable branes. Our analysis is based on standard worldsheet methods in the context of non-critical bosonic string theory. The stable branes have Neumann (FZZT) boundary conditions in the Liouville direction. Several generalizations are possible.

We study the relationship of soliton solutions for electron system with those of the sigma model on the noncommutative space, working directly in the operator formalism. We find that some soliton solutions of the sigma model are also the solitons of the electron system and are classified by the same topological numbers.

The possibility that the Gallium data effectively indicates a time modulation of the solar active neutrino flux in possible connection to solar activity is examined on the light of spin flavour precession to sterile neutrinos as a subdominant process in addition to oscillations. We distinguish two sets of Gallium data, relating them to high and low solar activity. Such modulation affects principally the low energy neutrinos (pp and ⁷Be) so that the effect, if it exists, will become most clear in the forthcoming Borexino and LENS experiments and will provide evidence for a neutrino magnetic moment. Using a model previously developed, we perform two separate fits in relation to low and high activity periods to all solar neutrino data. These fits include the very recent charged current spectrum from the SNO experiment. We also derive the model predictions for Borexino and LENS experiments.

We study a topological string description of the c < 1 non-critical string whose matter part is defined by the time-like linear dilaton CFT. We show that the topologically twisted N = 2 SL(2,)/U(1) model (or supersymmetric 2D black hole) is equivalent to the c < 1 non-critical string compactified at a specific radius by comparing their physical spectra and correlation functions. We examine another equivalent description in the topological Landau-Ginzburg model and check that it reproduces the same scattering amplitudes. We also discuss its matrix model dual description.

Spontaneously broken family symmetry provides a promising origin for the observed quark and lepton mass and mixing angle structure. In a supersymmetric theory such structure comes from a combination of the contributions from the superpotential and the Kähler potential. The superpotential effects have been widely studied but relatively little attention has been given to the effects of the Kähler sector. In this paper we develop techniques to simplify the analysis of such Kähler effects. Using them we show that in the class of theories with an hierarchical structure for the Yukawa couplings the Kähler corrections to both the masses and mixing angles are subdominant. This is true even in cases that texture zeros are filled in by the terms coming from the Kähler potential.

We consider the mechanism of screening of the Dirac flavor structure in the context of the double seesaw mechanism. As a consequence of screening, the structure of the light neutrino mass matrix, m_ν, is determined essentially by the structure of the (Majorana) mass matrix, M_S, of new super-heavy (Planck scale) neutral fermions S. We calculate effects of the renormalization group running in order to investigate the stability of the screening mechanism with respect to radiative corrections. We find that screening is stable in the supersymmetric case, whereas in the standard model it is unstable for certain structures of M_S. The screening mechanism allows us to reconcile the (approximate) quark-lepton symmetry and the strong difference of the mixing patterns in the quark and lepton sectors. It opens new possibilities to explain a quasi-degenerate neutrino mass spectrum, special ``neutrino'' symmetries and quark-lepton complementarity. Screening can emerge from certain flavor symmetries or Grand Unification.

The quadratic α' corrections to the two-dimensional black hole and to its T-dual are calculated. These backgrounds are used to write the covariant form of the α'² corrections to the T-duality for general time-dependent backgrounds of dilaton and diagonal metric in the bosonic string theory.

In supersymmetric models with gravity-mediated SUSY breaking and gaugino mass unification, the predicted relic abundance of neutralinos usually exceeds the strict limits imposed by the WMAP collaboration. One way to obtain the correct relic abundance is to abandon gaugino mass universality and allow a mixed wino-bino lightest SUSY particle (LSP). The enhanced annihilation and scattering cross sections of mixed wino dark matter (MWDM) compared to bino dark matter lead to enhanced rates for direct dark matter detection, as well as for indirect detection at neutrino telescopes and for detection of dark matter annihilation products in the galactic halo. For collider experiments, MWDM leads to a reduced but significant mass gap between the lightest neutralinos so that ₂two-body decay modes are usually closed. This means that dilepton mass edges– the starting point for cascade decay reconstruction at the CERN LHC– should be accessible over almost all of parameter space. Measurement of the m₂−m₁ mass gap at LHC plus various sparticle masses and cross sections as a function of beam polarization at the International Linear Collider (ILC) would pinpoint MWDM as the dominant component of dark matter in the universe.

We analyze in detail the relation between an exactly marginal deformation of = 4 SYM — the Leigh-Strassler or ``β-deformation'' — and its string theory dual (recently constructed in hep-th/0502086) by comparing energies of semiclassical strings to anomalous dimensions of gauge-theory operators in the two-scalar sector. We stress the existence of integrable structures on the two sides of the duality. In particular, we argue that the integrability of strings in AdS₅ × S⁵ implies the integrability of the deformed world sheet theory with real deformation parameter. We compare the fast string limit of the worldsheet action in the sector with two angular momenta with the continuum limit of the coherent state action of an anisotropic XXZ spin chain describing the one-loop anomalous dimensions of the corresponding operators and find a remarkable agreement for all values of the deformation parameter. We discuss some of the properties of the Bethe Ansatz for this spin chain, solve the Bethe equations for small number of excitations and comment on higher loop properties of the dilatation operator. With the goal of going beyond the leading order in the 't Hooft expansion we derive the analog of the Bethe equations on the string-theory side, and show that they coincide with the thermodynamic limit of the Bethe equations for the spin chain. We also compute the 1/J corrections to the anomalous dimensions of operators with large R-charge (corresponding to strings with angular momentum J) and match them to the 1-loop corrections to the fast string energies. Our results suggest that the impressive agreement between the gauge theory and semiclassical strings in AdS₅ × S⁵ is part of a larger picture underlying the gauge/gravity duality.

The correspondences proposed previously between higher spin gauge theories and free singleton field theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D = 4 to include the strongly coupled fixed point of the 3d O(N) vector model. Here we propose an = 1 supersymmetric version of this picture. We also elaborate on the role of parity in constraining the bulk interactions, and in distinguishing two minimal bosonic models obtained as two different consistent truncations of the minimal N = 1 model that retain the scalar or the pseudo-scalar field. We refer to these models as the type-A and type-B models, respectively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the type-A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture.

In pure = 1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate the N vacua have been argued, on the basis of string theory realizations, to be D-branes for the confining string. In a certain limit, this means that a configuration of k parallel domain walls is described by a 2+1-dimensional U(k) gauge theory. This theory has been identified by Acharya and Vafa as the U(k) gauge theory with 4 supercharges broken by a Chern-Simons term of level N in such a way that 2 supercharges are preserved. We argue further that the gauge coupling of the domain wall gauge theory goes like g² ∼ Λ/N , for large N. In the case of two domain walls, we show that the U(2) world-volume theory generates a quadratic potential on the Coulomb branch at two loops in perturbation theory which is consistent with there being a supersymmetric bound state of the two wall system. A mass gap of order Λ/Nis generated around the supersymmetric minimum and we estimate the size of the bound-state to be order Λ/(N)^1/2. At large distance the potential reaches a constant that can qualitatively account for the binding energy of the two walls even though stringy effects are not, strictly speaking, decoupled.

We exhibit a new consistent group-manifold reduction of pure Einstein gravity in the vielbein formulation when the compactification group manifold is S³. The novel feature in the reduction is to exploit the two 3-dimensional Lie algebras that S³ admits. The first algebra is introduced into the group-manifold reduction in the standard way through the Maurer-Cartan 1-forms associated to the symmetry of the general coordinate transformations. The second algebra is associated to the linear adjoint group and it is introduced into the group-manifold reduction through a local transformation in the internal tangent space. We discuss the characteristics of the resulting lower-dimensional theory and we emphasize the novel results generated by the new group-manifold reduction. As an application of the reduction we show that the lower-dimensional theory admits a domain wall solution which upon uplifting to the higher-dimension results to be the self-dual (in the non-vanishing components of both curvature and spin connection) Kaluza-Klein monopole. This discussion may be relevant in the dimensional reductions of M-theory, string theory and also in the Bianchi cosmologies in four dimensions.

We identify scenarios not ruled out by LEP data in which NMSSM Higgs detection at the LHC will be particularly challenging. We first review the `no-lose' theorem for Higgs discovery at the LHC that applies if Higgs bosons do not decay to other Higgs bosons — namely, with L = 300 fb<sup>-1</sup>, there is always one or more `standard' Higgs detection channel with at least a 5σ signal. However, we provide examples of no-Higgs-to-Higgs cases for which all the standard signals are no larger than 7σ implying that if the available L is smaller or the simulations performed by ATLAS and CMS turn out to be overly optimistic, all standard Higgs signals could fall below 5σ even in the no-Higgs-to-Higgs part of NMSSM parameter space. In the vast bulk of NMSSM parameter space, there will be Higgs-to-Higgs decays. We show that when such decays are present it is possible for all the standard detection channels to have very small significance. In most such cases, the only strongly produced Higgs boson is one with fairly SM-like couplings that decays to two lighter Higgs bosons (either a pair of the lightest CP-even Higgs bosons, or, in the largest part of parameter space, a pair of the lightest CP-odd Higgs bosons). A number of representative bench-mark scenarios of this type are delineated in detail and implications for Higgs discovery at various colliders are discussed.

We define U(n) gauge theory on fuzzy S²_N × S²_N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S² × S² in the commutative limit N→∞. The model can be used as a regularization of gauge theory on noncommutative ⁴_θ in a particular scaling limit, which is studied in detail. We also find topologically non-trivial U(1) solutions, which reduce to the known ``fluxon'' solutions in the limit of ⁴_θ, reproducing their full moduli space. Other solutions which can be interpreted as 2-dimensional branes are also found. The quantization of the model is defined non-perturbatively in terms of a path integral which is finite. A gauge-fixed BRST-invariant action is given as well. Fermions in the fundamental representation of the gauge group are included using a formulation based on SO(6), by defining a fuzzy Dirac operator which reduces to the standard Dirac operator on S² × S² in the commutative limit. The chirality operator and Weyl spinors are also introduced.

We present a solution of the vacuum Einstein's equations in five dimensions corresponding to a black ring with horizon topology S¹ × S² and rotation in the azimuthal direction of the S². This solution has a regular horizon up to a conical singularity, which can be placed either inside the ring or at infinity. This singularity arises due to the fact that this black ring is not balanced. In the infinite radius limit we correctly reproduce the Kerr black string, and taking another limit we recover the Myers-Perry black hole with a single angular momentum.

In this paper we re-derive the effective Nambu-Goto theory result for the Polyakov loop correlator, starting from the free bosonic string and using a covariant quantization. The boundary conditions are those of an open string attached to two D0-branes at spatial distance R, in a target space with compact euclidean time. The one-loop free energy contains topologically distinct sectors corresponding to multiple covers of the cylinder in target space bordered by the Polyakov loops. The sector that winds once reproduces exactly the Nambu-Goto partition function. In our approach, the world-sheet duality between the open and closed channel is most evident and allows for an explicit interpretation of the free energy in terms of tree level exchange of closed strings between boundary states. Our treatment is fully consistent only in d = 26; extension to generic d may be justified for large R, and is supported by Montecarlo data. At shorter scales, consistency and Montecarlo data seem to suggest the necessity of taking into account the Liouville mode of Polyakov's formulation.

We explore the description of bulk causal structure in a dual field theory. We observe that in the spacetime dual to a spacelike non-commutative field theory, the causal structure in the boundary directions is modified asymptotically. We propose that this modification is described in the dual theory by a modification of the micro-causal light cone. Previous studies of this micro-causal light cone for spacelike non-commutativite field theories agree with the expectations from the bulk spacetime. We describe the spacetime dual to field theories with lightlike non-commutativity, and show that they generically have a drastic modification of the light cone in the bulk: the spacetime is non-distinguishing. This means that the spacetime while being devoid of closed timelike or null curves, has causal curves that are ``almost closed''. We go on to show that the micro-causal light cone in the field theory agrees with this prediction from the bulk.

We study the tachyon and the RR field sourced by the (m,n) ZZ D-branes in type 0 theories using three methods. We first use the mini-superspace approximation of the closed string wave functions of the tachyon and the RR scalar to probe these fields. These wave functions are then extended beyond the mini-superspace approximation using mild assumptions which are motivated by the properties of the corresponding wave functions in the mini-superspace limit. These are then used to probe the tachyon and the RR field sourced. Finally we study the space time fields sourced by the (m,n) ZZ D-branes using the FZZT brane as a probe. In all the three methods we find that the tension of the (m,n) ZZ brane is mn times the tension of the (1,1) ZZ brane. The RR charge of these branes is non-zero only for the case of both m and n odd, in which case it is identical to the charge of the (1,1) brane. As a consistency check we also verify that the space time fields sourced by the branes satisfy the corresponding equations of motion.

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labelled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.

We consider the possibility of neutrinos being Dirac particles and study minimal mass matrices with as much zero entries as possible. We find that up to 5 zero entries are allowed. Those matrices predict one vanishing mass state, CP conservation and U_e3 either zero or proportional to R, where R is the ratio of the solar and atmospheric Δm². Matrices containing 4 zeros can be classified in categories predicting U_e3 = 0, U_e3≠0 but no CP violation or |U_e3|≠0 and possible CP violation. Some cases allow to set constraints on the neutrino masses. The characteristic value of U_e3 capable of distinguishing some of the cases with non-trivial phenomenological consequences is about R/2 sin 2θ₁₂. Matrices containing 3 and less zero entries imply (with a few exceptions) no correlation for the observables. We outline models leading to the textures based on the Froggatt-Nielsen mechanism or the non-abelian discrete symmetry D₄ × Z₂.

Universal extra dimensions and supersymmetry have rather similar experimental signatures at hadron colliders. The proper interpretation of an LHC discovery in either case may therefore require further data from a lepton collider. In this paper we identify methods for discriminating between the two scenarios at the linear collider. We study the processes of Kaluza-Klein muon pair production in universal extra dimensions in parallel to smuon pair production in supersymmetry, accounting for the effects of detector resolution, beam-beam interactions and accelerator induced backgrounds. We find that the angular distributions of the final state muons, the energy spectrum of the radiative return photon and the total cross-section measurement are powerful discriminators between the two models. Accurate determination of the particle masses can be obtained both by a study of the momentum spectrum of the final state leptons and by a scan of the particle pair production thresholds. We also calculate the production rates of various Kaluza-Klein particles and discuss the associated signatures.

We generate new 11-dimensional supergravity solutions from deformations based on U(1)³ symmetries. The initial geometries are of the form AdS₄ × Y₇, where Y₇ is a 7-dimensional Sasaki-Einstein space. We consider a general family of cohomogeneity one Sasaki-Einstein spaces, as well as the recently-constructed cohomogeneity three L^p,q,r,s spaces. For certain cases, such as when the Sasaki-Einstein space is S⁷, Q^1,1,1 or M^1,1,1, the deformed gravity solutions correspond to a marginal deformation of a known dual gauge theory.

We investigate the properties of the AdS D1-branes which are the bound states of a curved D1-brane with n fundamental strings (F1) in the AdS₃ spacetime, and the AdS D2-branes which are the axially symmetric bound states of a curved D2-brane with m D0-branes and n fundamental strings in the AdS₃ × S³ spacetime. We see that, while the AdS D1-branes asymptotically approach to the event horizon of the AdS₃ spacetime the AdS D2-branes will end on it. As the near horizon geometry of the F1/NS5 becomes the spacetime of AdS₃ × S³ × T⁴ with NS-NS three form turned on, we furthermore investigate the corresponding AdS D-branes in the NS5-branes and macroscopic F-strings backgrounds, as an attempt to understand the origin of the AdS D-branes. From the found DBI solutions we see that in the F-strings background, both of the AdS D1-branes and AdS D2-branes will asymptotically approach to the position with a finite distance away from the F-strings. However, the AdS D2-branes therein could also end on the F-strings once it carries sufficient D0-branes charges. We also see that there does not exist any stable AdS D-branes in the NS5-branes backgrounds. We present physical arguments to explain these results, which could help us in understanding the intriguing mechanics of the formation of the AdS D-branes.

We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop = 4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS₅ × S⁵ derived in [64]. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying (2,2|4) superalgebra, in particular of the type ``Beauty'' and ``Beast''.

We study the universal low-energy dynamics associated with the spontaneous breaking of Lorentz invariance down to spatial rotations. The effective lagrangian for the associated Goldstone field can be uniquely determined by the non-linear realization of a broken time diffeomorphism symmetry, up to some overall mass scales. It has previously been shown that this symmetry breaking pattern gives rise to a Higgs phase of gravity, in which gravity is modified in the infrared. In this paper, we study the effects of direct couplings between the Goldstone boson and standard model fermions, which necessarily accompany Lorentz-violating terms in the theory. The leading interaction is the coupling to the axial vector current, which reduces to spin in the non-relativistic limit. A spin moving relative to the ``ether" rest frame will emit Goldstone Cerenkov radiation. The Goldstone also induces a long-range inverse-square law force between spin sources with a striking angular dependence, reflecting the underlying Goldstone shockwaves and providing a smoking gun for this theory. We discuss the regime of validity of the effective theory describing these phenomena, and the possibility of probing Lorentz violations through Goldstone boson signals in a way that is complementary to direct tests in some regions of parameter space.

Using the latest determinations of several theoretical and experimental parameters, we update the Unitarity Triangle analysis in the Standard Model. The basic experimental constraints come from the measurements of |V_ub/V_cb|, Δm_d, the lower limit on Δm_s, _K, and the measurement of the phase of the B_d–_dmixing amplitude through the time-dependent CP asymmetry in B⁰→J/ψK⁰ decays. In addition, we consider the direct determination of α, γ, 2β+γ and cos 2β from the measurements of new CP-violating quantities, recently performed at the B factories. We also discuss the opportunities offered by improving the precision of the various physical quantities entering in the determination of the Unitarity Triangle parameters. The results and the plots presented in this paper can also be found at the URL http://www.utfit.org , where they are continuously updated with the newest experimental and theoretical results.

In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents and Wilson-Fisher fixed points in three dimensions, providing a certain ``optimised'' cutoff is used for the Legendre flow equation. Here we point out that this is a consequence of an exact map between the two equations, which is nothing other than the exact reduction of the functional map that exists between the two exact renormalization groups. We note also that the optimised cutoff does not allow a derivative expansion beyond second order.

We find an explicit relation between the two known ways of generating an infinite set of local conserved charges for the string sigma model on AdS₅ × S⁵: the Bäcklund and monodromy approaches. We start by constructing the two-parameter family of Bäcklund transformations for the string with an arbitrary world-sheet metric. We then show that only for a special value of one of the parameters the solutions generated by this transformation are compatible with the Virasoro constraints. By solving the Bäcklund equations in a non-perturbative fashion, we finally show that the generating functional of the Bäcklund conservation laws is equal to a certain sum of the quasi-momenta. The positions of the quasi-momenta in the complex spectral plane are uniquely determined by the real parameter of the Bäcklund transform.

We derive general tree-level recursion relations for amplitudes which include massive propagating particles. As an illustration, we apply these recursion relations to scattering amplitudes of gluons coupled to massive scalars. We provide new results for all amplitudes with a pair of scalars and n ⩽ 4 gluons. These amplitudes can be used as building blocks in the computation of one-loop 6-gluon amplitudes using unitarity based methods.

Inspired by the AdS/CFT correspondence, we show that any G/H symmetry breaking pattern can be described by a simple two-site moose diagram. This construction trivially reproduces the CCWZ prescription in the context of Hidden Local Symmetry. We interpret this moose in a novel way to show that many little Higgs theories can emerge from ordinary chiral symmetry breaking in scaled-up QCD. We apply this reasoning to the simple group little Higgs to see that the same low energy degrees of freedom can arise from a variety of UV complete theories. We also show how models of holographic composite Higgs bosons can turn into brane-localized little technicolor theories by ``integrating in'' the IR brane.

A new variant of the supersymmetric fat Higgs model is presented in which the MSSM Higgses as well as the top quark are composite. The underlying theory is an s-confining SU(3) gauge theory with the MSSM gauge groups realized as gauged sub-groups of the chiral flavor symmetries. This motivates the large Yukawas necessary for the large top mass and SM-like Higgs of mass >> M_Z in a natural way as the residual of the strong dynamics responsible for the composites. This removes fine-tuning associated with these couplings present in the original fat Higgs and ``new fat Higgs'' models, respectively.

The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. In this work, we propose an efficient variational method based on the matrix product ansatz for a ₂ lattice gauge theory on a spatial ladder chain. Gauge invariant low-lying states are identified by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian.

We construct all connected toric phases of the recently discovered Y^p,q quivers and show their IR equivalence using Seiberg duality. We also compute the R and global U(1) charges for a generic toric phase of Y^p,q.

We study transverse-momentum-dependent (TMD) gluon distributions and related factorization theorems for gluon-initiated semi-inclusive processes at hadron colliders. Gauge-invariant TMD gluon distributions are introduced, and their relations to the integrated (Feynman) parton distributions are established when the transverse momentum is large. Through explicit calculations, soft-collinear factorization is verified at one-loop order for scalar particle (e.g. Higgs) production. Summation over large double logarithms is performed through solving Collins-Soper equation. We reproduce the known result in the limit that the transverse momentum of the scalar is large.

We construct a first order deformation of the complex structure of the cone over Sasaki-Einstein spaces Y^p,q and check supersymmetry explicitly. This space is a central element in the holographic dual of chiral symmetry breaking for a large class of cascading quiver theories. We discuss a solution describing a stack of N D3 branes and M fractional D3 branes at the tip of the deformed spaces.

The method to merge matrix elements for multi particle production and parton showers in e⁺e⁻ annihilations and hadronic collisions and its implementation into the new event generator SHERPA is described in detail. Examples highlighting different aspects of it are thoroughly discussed, some results for various cases are presented. In addition, a way to extend this method to general electroweak interactions is presented.

We argue that the closed string energy in the bulk bouncing tachyon background is to be quantised in a simple manner as if strings were trapped in a finite time interval. We discuss it from three different viewpoints; (1) the timelike continuation of the sinh-Gordon model, (2) the dual matrix model description of the (1+1)-dimensional string theory with the bulk bouncing tachyon condensate, (3) the c_L = 1 limit of the timelike Liouville theory with the dual Liouville potential turned on. There appears to be a parallel between the bulk bouncing tachyon and the full S-brane of D-brane decay. We find the critical value λ_c of the bulk bouncing tachyon coupling which is analogous to λ_o = 1/2 of the full S-brane coupling, at which the system is thought to be at the bottom of the tachyon potential.

PHASE is a new event generator dedicated to the study of Standard Model processes with six fermions in the final state at the LHC. The code is intended for analyses of vector boson scattering, Higgs search, three gauge boson production, and top physics. This first version of the program describes final states characterized by the presence of one neutrino, pp→4q+lν_l , at (α⁶ ). PHASE is based on a new iterative-adaptive multichannel technique, and employs exact leading order matrix elements. The code can generate unweighted events for any subset of all available final states. The produced parton-level events carry full information on their colour and flavour structure, enabling the evolution of the partons into fully hadronised final states. An interface to hadronization packages is provided via the Les Houches Protocol.

We investigate the possible existence of the spin 3/2 pentaquark states using interpolating currents with K-N color-octet structure in the framework of QCD finite energy sum rule (FESR). We pay special attention to the convergence of the operator product expansion.

With respect to the question of supersymmetry breaking, there are three branches of the flux landscape. On one of these, if one requires small cosmological constant, supersymmetry breaking is predominantly at the fundamental scale; on another, the distribution is roughly flat on a logarithmic scale; on the third, the preponderance of vacua are at very low scale. A priori, as we will explain, one can say little about the first branch. The vast majority of these states are not accessible even to crude, approximate analysis. On the other two branches one can hope to do better. But as a result of the lack of access to branch one, and our poor understanding of cosmology, we can at best conjecture about whether string theory predicts low energy supersymmetry or not. If we hypothesize that are on branch two or three, distinctive predictions may be possible. We comment of the status of naturalness within the landscape, deriving, for example, the statistics of the first branch from simple effective field theory reasoning.

One of the most precise measurements of the strong coupling constant α_s(M_Z) is obtained in the context of global analyses of precision electroweak data. This article reviews the sensitivity of different electroweak observables to α_s and describes the perturbative uncertainties related to missing higher orders. The complete renormalisation scale dependence for the relevant observables is calculated at next-to-next-to-leading order and a new method is presented to determine the corresponding perturbative uncertainty for measurements of α_s based on these observables.

The description of B-type D-branes on a tensor product of two N = 2 minimal models in terms of matrix factorisations is related to the boundary state description in conformal field theory. As an application we show that the D0- and D2-brane for a number of Gepner models are described by permutation boundary states. In some cases (including the quintic) the images of the D2-brane under the Gepner monodromy generate the full charge lattice.

Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in the box and the two-channel S-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known Lüscher's formula which establishes a similar relation in elastic scattering.

We investigate D-branes in a ₃ × ₃ orbifold with discrete torsion. For this class of orbifolds the only known objects which couple to twisted RR potentials have been non-BPS branes. By using more general gluing conditions we construct here a D-brane which is BPS and couples to RR potentials in the twisted and in the untwisted sectors.

Black branes and strings are generally unstable against a certain sector of gravitational perturbations. This is known as the Gregory-Laflamme instability. It has been recently argued [1], [2] that there exists another general instability affecting many rotating extended black objects. This instability is in a sense universal, in that it is triggered by any massless field, and not just gravitational perturbations. Here we investigate this novel mechanism in detail. For this instability to work, two ingredients are necessary: (i) an ergo-region, which gives rise to superradiant amplification of waves, and (ii) ``bound'' states in the effective potential governing the evolution of the particular mode under study. We show that the black brane Kerr₄×R^p is unstable against this mechanism, and we present numerical results for instability timescales for this case. On the other hand, and quite surprisingly, black branes of the form Kerr_d×R^p are all stable against this mechanism for d > 4. This is quite an unexpected result, and it stems from the fact that there are no stable circular orbits in higher dimensional black hole spacetimes, or in a wave picture, that there are no bound states in the effective potential. We also show that it is quite easy to simulate this instability in the laboratory with acoustic black branes.

Large N coherent state methods are used to study the relation between U(N_c) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N_c limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N_c dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N_c dynamics of the daughter theory, restricted to the untwisted sector invariant under ``theory space'' permutations, coincide. This implies equality, in the large N_c limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N_c equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N_c equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling [1].

We present a new normalization condition for the axial current, derived from the PCAC relation with non-vanishing quark mass. This condition is expected to reduce mass effects in the chiral extrapolation of the results for the normalization factor Z_A. The application to the two-flavor theory with improved Wilson fermions shows that this expectation is indeed fulfilled. Using the Schrödinger functional setup we calculate Z_A(g₀²) as well as the vector current normalization factor Z_V(g₀²) for β = 6/g₀² ⩾ 5.2.

We study static, spherically symmetric, composite global-local monopoles with a direct interaction term between the two sectors in the regime where the interaction potential is large. At some critical coupling the global defect disappears and with it the deficit angle of the space-time. We find new solutions which represent local monopoles in an Anti-de-Sitter spacetime. In another parameter range the magnetic monopole, or even both, disappear. The decay of the magnetic monopole is accompanied by a dynamical transition from the higgsed phase to the gauge-symmetric phase. We comment on the applications to cosmology, topological inflation and braneworlds

Several functional renormalisation group (RG) equations including Polchinski flows and Exact RG flows are compared from a conceptual point of view and in given truncations. Similarities and differences are highlighted with special emphasis on stability properties. The main observations are worked out at the example of O(N) symmetric scalar field theories where the flows, universal critical exponents and scaling potentials are compared within a derivative expansion. To leading order, it is established that Polchinski flows and ERG flows — despite their inequivalent derivative expansions — have identical universal content, if the ERG flow is amended by an adequate optimisation. The results are also evaluated in the light of stability and minimum sensitivity considerations. Extensions to higher order and further implications are emphasized.

We use the twistor-string theory on the B-model of CP^3|4to compute the maximally helicity violating(MHV) tree amplitudes for conformal supergravitons. The correlator of a bilinear in the affine Kac-Moody current(Sugawara stress-energy tensor) can generate these amplitudes. We compare with previous results from open string version of twistor-string theory. We also compute the MHV tree amplitudes for both gravitons and gluons from the correlators between stress-energy tensor and current.

We present a non-compact 4 + 1 dimensional model with a local strong four-fermion interaction supplementing it with gravity. In the strong coupling regime it reveals the spontaneous translational symmetry breaking which eventually leads to the formation of domain walls, or thick 3-branes, embedded in the AdS₅ manifold. To describe this phenomenon we construct the appropriate low-energy effective Action and find kink-like vacuum solutions in the quasi-flat riemannian metric. We discuss the generation of ultra-low-energy 3 + 1 dimensional physics and we establish the relation among the bulk five dimensional gravitational constant, the brane Newton's constants and the curvature of AdS₅ space-time. The plausible relation between the compositeness scale of the scalar matter and the symmetry breaking scale is shown to support the essential decoupling of branons, the scalar fluctuations of the brane, from the Standard Model matter, supporting their possible role in the dark matter saturation. The induced cosmological constant on the brane does vanish due to exact cancellation of matter and gravity contributions.

We explore integrability properties of superstring equations of motion in AdS₅ × S⁵. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding hamiltonian dynamics on subspace of physical superstring degrees of freedom. We present some explicit results for the corresponding conserved charges by consistently reducing the dynamics to AdS₃ × S³ and AdS₃ × S¹ subsectors containing both bosonic and fermionic fields.

We solve the A_2n⁽²⁾ vertex model with all kinds of diagonal reflecting matrices by using the algebraic Bethe ansatz, which includes constructing the multi-particle states and achieving the eigenvalue of the transfer matrix and corresponding Bethe ansatz equations. When the model is U_q(B_n) quantum invariant, our conclusion agrees with that obtained by analytic Bethe ansatz method.