Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence

Dimofte, Tudor

doi:10.1007/s00220-015-2401-1

Title: Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence

Journal Article · Tue Jun 16 00:00:00 EDT 2015 · Communications in Mathematical Physics

DOI:https://doi.org/10.1007/s00220-015-2401-1· OSTI ID:1598859

Dimofte, Tudor ^[1]

Institute for Advanced Study, Princeton, NJ (United States)

Herein, we use the 3d–3d correspondence together with the DGG construction of theories T _n[M] labelled by 3-manifolds M to define a non-perturbative state-integral model for ${SL(n,\mathbb{C})}$ Chern–Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k = 1 state-integral, as well as the 3d index, which is k = 0. The Chern–Simons partition functions correspond to partition functions of T_n[M] on squashed lens spaces L(k, 1). At any k, they admit a holomorphic-antiholomorphic factorization, corresponding to the decomposition of L(k, 1) into two solid tori, and the associated holomorphic block decomposition of the partition functions of T_n[M]. A generalization to L(k, p) is also introduced. Convergence of the state integrals, for any k, requires triangulations to admit a positive angle structure; we propose that this is also necessary for the DGG gauge theoryT_n[M] to flow to a desired IR SCFT.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0009988

OSTI ID:: 1598859

Journal Information:: Communications in Mathematical Physics, Vol. 339, Issue 2; ISSN 0010-3616

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 47 works

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Quantisation of Super Teichmüller Theory Pawelkiewicz, Michal; Aghaei, Nezhla; Teschner, Jörg Springer https://doi.org/10.7892/boris.102360	text	January 2017
K-Decompositions and 3d Gauge Theories Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B. arXiv https://doi.org/10.48550/arxiv.1301.0192	preprint	January 2013
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Title: Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence

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