002629915 001__ 2629915
002629915 005__ 20240830063754.0
002629915 0248_ $$aoai:cds.cern.ch:2629915$$pcerncds:CERN$$pcerncds:CERN:FULLTEXT$$pcerncds:FULLTEXT
002629915 0247_ $$2DOI$$9bibmatch$$a10.1007/JHEP11(2018)004
002629915 037__ $$9arXiv$$aarXiv:1807.02328$$chep-th
002629915 037__ $$9arXiv:reportnumber$$aCERN-TH-2018-156
002629915 035__ $$9arXiv$$aoai:arXiv.org:1807.02328
002629915 035__ $$9Inspire$$aoai:inspirehep.net:1681291$$d2024-08-29T00:55:43Z$$h2024-08-30T02:32:46Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002629915 035__ $$9Inspire$$a1681291
002629915 041__ $$aeng
002629915 100__ $$aClosset, Cyril$$tGRID:grid.9132.9$$uCERN$$vTheory Department, Mathematical Institute, University of Oxford Woodstock Road, Geneva 23, CERN CH-1211, OX2 6GG, 93106 Oxford, Santa Barbara, Switzerland, United Kingdom
002629915 245__ $$9arXiv$$aSeifert fibering operators in 3d $\mathcal{N}=2$ theories
002629915 269__ $$c2018-07-06
002629915 260__ $$c2018-11-05
002629915 300__ $$a135 p
002629915 500__ $$9arXiv$$a135 pages + appendix; v2: fixed typos, added references, small
corrections in section 9
002629915 520__ $$9Springer$$aWe study 3d $ \mathcal{N}=2 $ supersymmetric gauge theories on closed oriented Seifert manifolds — circle bundles over an orbifold Riemann surface —, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. Our main result is an exact formula for the supersymmetric partition function on any Seifert manifold, generalizing previous results on lens spaces. We explain how the result for an arbitrary Seifert geometry can be obtained by combining simple building blocks, the “fibering operators.” These operators are half-BPS line defects, whose insertion along the S$^{1}$ fiber has the effect of changing the topology of the Seifert fibration. We also point out that most supersymmetric partition functions on Seifert manifolds admit a discrete refinement, corresponding to the freedom in choosing a three-dimensional spin structure. As a strong consistency check on our result, we show that the Seifert partition functions match exactly across infrared dualities. The duality relations are given by intricate (and seemingly new) mathematical identities, which we tested numerically. Finally, we discuss in detail the supersymmetric partition function on the lens space L(p, q)$_{b}$ with rational squashing parameter b$^{2}$ ∈ ℚ, comparing our formalism to previous results, and explaining the relationship between the fibering operators and the three-dimensional holomorphic blocks.
002629915 520__ $$9arXiv$$aWe study 3d $\mathcal{N}=2$ supersymmetric gauge theories on closed oriented Seifert manifold---circle bundles over an orbifold Riemann surface---, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. Our main result is an exact formula for the supersymmetric partition function on any Seifert manifold, generalizing previous results on lens spaces. We explain how the result for an arbitrary Seifert geometry can be obtained by combining simple building blocks, the "fibering operators." These operators are half-BPS line defects, whose insertion along the $S^1$ fiber has the effect of changing the topology of the Seifert fibration. We also point out that most supersymmetric partition functions on Seifert manifolds admit a discrete refinement, corresponding to the freedom in choosing a three-dimensional spin structure. As a strong consistency check on our result, we show that the Seifert partition functions match exactly across infrared dualities. The duality relations are given by intricate (and seemingly new) mathematical identities, which we tested numerically. Finally, we discuss in detail the supersymmetric partition function on the lens space $L(p,q)_b$ with rational squashing parameter $b^2 \in \mathbb{Q}$, comparing our formalism to previous results, and explaining the relationship between the fibering operators and the three-dimensional holomorphic blocks.
002629915 540__ $$3preprint$$aarXiv nonexclusive-distrib 1.0$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002629915 540__ $$3publication$$aCC-BY-4.0$$bSpringer
002629915 595__ $$aCERN-TH
002629915 65017 $$2arXiv$$ahep-th
002629915 65017 $$2SzGeCERN$$aParticle Physics - Theory
002629915 690C_ $$aCERN
002629915 690C_ $$aARTICLE
002629915 700__ $$aKim, Heeyeon$$tGRID:grid.4991.5$$uOxford U., Inst. Math.$$vMathematical Institute, University of Oxford Woodstock Road, OX2 6GG, 93106 Oxford, United Kingdom
002629915 700__ $$aWillett, Brian$$tGRID:grid.133342.4$$uSanta Barbara, KITP$$vKavli Institute for Theoretical Physics - California U. - Santa Barbara - CA - 93106 - U.S.A.
002629915 773__ $$c004$$pJHEP$$v11$$y2018
002629915 8564_ $$81418672$$s3219280$$uhttp://cds.cern.ch/record/2629915/files/1807.02328.pdf$$yFulltext
002629915 8564_ $$81418673$$s14286$$uhttp://cds.cern.ch/record/2629915/files/blockfig8.png$$y00007 : \;
002629915 8564_ $$81418674$$s63659$$uhttp://cds.cern.ch/record/2629915/files/T10.png$$y00004 : \small $T(1,0)$. : \small $T(2,1)$.
002629915 8564_ $$81418675$$s9501$$uhttp://cds.cern.ch/record/2629915/files/blockfig5.png$$y00001 : \;
002629915 8564_ $$81418676$$s5303$$uhttp://cds.cern.ch/record/2629915/files/blockfig6.png$$y00002 : On the left, the contour $\Gamma_\alpha$ is shown for finite $\tau$, with towers of poles separated by $\tau$. As $\tau$ becomes small, the contributions from $\hat{u}$ and its images are dominant, shown in red. On the right, we take the $\tau \rightarrow 0$ limit, where we may approximate the answer by the contribution from $u=\hat{u}$. Here the towers of poles have collapsed to form the branch cuts of $\cW(u)$. : Caption not extracted
002629915 8564_ $$81418677$$s18803$$uhttp://cds.cern.ch/record/2629915/files/blockfig7.png$$y00003 Contour $\Gamma_\alpha$ corresponding to a block $B_{\t g}$ with non trivial $(q,p)$, at finite $\tau$.
002629915 8564_ $$81418678$$s69725$$uhttp://cds.cern.ch/record/2629915/files/T21.png$$y00000 : \small $T(3,2)$. : Solid fibered tori $T(q,t)$. The central fiber, shown in red, is exceptional if $q>1$. Generic fibers are shown in black.
002629915 8564_ $$81418679$$s5601$$uhttp://cds.cern.ch/record/2629915/files/blockfig9.png$$y00005 : In the limit $\tau \rightarrow 0$, the dominant contributions to the integral over $\Gamma_\alpha$ come from the regions around $\hat{u}$ and their images. These can be reassembled into a series of $q$ shifted copies of contours passing through the critical points $u=q\tilde{u} = \hat{u}, \hat{u}+1,...,\hat{u}+q-1$. : Caption not extracted
002629915 8564_ $$81418680$$s74837$$uhttp://cds.cern.ch/record/2629915/files/T32.png$$y00006 : Caption not extracted
002629915 8564_ $$81447307$$s2709679$$uhttp://cds.cern.ch/record/2629915/files/scoap3-fulltext.pdf?subformat=pdfa$$xpdfa$$yArticle from SCOAP3
002629915 8564_ $$82333793$$s2709679$$uhttp://cds.cern.ch/record/2629915/files/scoap.pdf$$yArticle from SCOAP3
002629915 960__ $$a13
002629915 980__ $$aARTICLE