APS : Running of gauge couplings in string theory

Abel, Steven; Nutricati, Luca A.; Dienes, Keith R.

doi:10.1103/PhysRevD.107.126019

Article
Report number	arXiv:2303.08534 ; CERN-TH-2023-044 ; IPPP/23/16
Title	Running of gauge couplings in string theory
Related title	On the Running of Gauge Couplings in String Theory
Author(s)	Abel, Steven (Durham U., IPPP ; Durham U., Dept. of Math. ; CERN) ; Dienes, Keith R. (Arizona U. ; Maryland U.) ; Nutricati, Luca A. (Durham U., IPPP ; Durham U., Dept. of Math.)
Publication	2023-06-15
Imprint	2023-03-15
Number of pages	38
Note	37 pages, LaTeX, 5 figures
In:	Phys. Rev. D 107 (2023) 126019
DOI	10.1103/PhysRevD.107.126019 (publication)
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-th ; Particle Physics - Theory
Abstract	In this paper we conduct a general, model-independent analysis of the running of gauge couplings within closed string theories. Unlike previous discussions in the literature, our calculations fully respect the underlying modular invariance of the string and include the contributions from the infinite towers of string states which are ultimately responsible for many of the properties for which string theory is famous, including an enhanced degree of finiteness and UV/IR mixing. In order to perform our calculations, we adopt a formalism that was recently developed for calculations of the Higgs mass within such theories, and demonstrate that this formalism can also be applied to calculations of gauge couplings. In general, this formalism gives rise to an ``on-shell'' effective field theory (EFT) description in which the final results are expressed in terms of supertraces over the physical string states, and in which these quantities exhibit an EFT-like ``running'' as a function of an effective spacetime mass scale. We find, however, that the calculation of the gauge couplings differs in one deep way from that of the Higgs mass: while the latter results depend on purely on-shell supertraces, the former results have a different modular structure which causes them to depend on off-shell supertraces as well. In some regions of parameter space, our results demonstrate how certain expected field-theoretic behaviors can emerge from the highly UV/IR-mixed environment. In other situations, by contrast, our results give rise to a number of intrinsically stringy behaviors that transcend what might be expected within an effective field theory approach.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: Published by the American Physical Society (License: CC BY 4.0), sponsored by SCOAP³

$Distinct steps associated with our analysis of an arbitrary physical quantity, as discussed in the text. The particular sequence of steps to be followed depends on the goal of the analysis. Particularly relevant results are those in the lower portions of this sketch, in which our physical quantity is expressed purely in terms of contributions from on-shell, physical string states and also in a form which runs as a function of a spacetime mass scale $\mu$.$ $The infinite sums $f_\beta(\tau_2)$ in Eq.~(\ref{lookslikesupertrace}), plotted as functions of $\tau_2$ for $0\leq \beta\leq 6$. The $\beta=0$ curve is the upper blue curve which asymptotes to $1$ as $\tau_2\to \infty$, while the $\beta=1,2,...,6$ curves all asymptote to $0$ as $\tau_2\to \infty$ and can be identified according to the increasing values that they have at any fixed large value of $\tau_2$ (with $n=1$ orange, $n=2$ green, $n=3$ red, {\it etc.}\/). As $\tau_2$ drops to zero from a large value, we see that our functions $f_\beta(\tau_2)$ do not diverge (as would have been expected as we slowly remove the $\tau_2$ cutoff), but instead remain within the bounds indicated in Eq.~(\ref{upperbound}), leading to finite values for $f_\beta(\tau_2)$ as $\tau_2\to 0$.$ $String states arranged as a matrix according to their right-moving (vertical) and left-moving (horizontal) worldsheet energies $(m,n)\equiv (p-r,p)$, respectively. The states with $r=0$ lie along the principal diagonal, while the states with $r=1,2,...$ lie along successive shifted diagonals. The requirement $r\geq 0$ selects only those string states along or above the principal diagonal, and the $\tau\to \tau+1$ invariance of the partition function ensures that only those ``squares'' shaded in green with $m-n\in\mathbbZ$ can be populated. The pink square is necessarily empty in any tachyon-free theory, and the row shaded in orange is excluded for heterotic strings because such strings have right-moving worldsheet energies $\geq -1/2$. In drawing this figure we have assumed that states populate only integer or half-integer mass levels, but in general the spectrum of states can be far denser and may even approach a continuum in $(m,n)$ [or equivalently in $p$] for exceedingly large or small compactification radii.$ Show more plots

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記錄創建於2023-03-17，最後更新在2023-07-08

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