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3d-3d correspondence for mapping tori

Chun, Sungbong and Gukov, Sergei and Park, Sunghyuk and Sopenko, Nikita (2020) 3d-3d correspondence for mapping tori. Journal of High Energy Physics, 2020 (9). Art. No. 152. ISSN 1029-8479. doi:10.1007/jhep09(2020)152.

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One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N = 2 SCFT T [M₃] — or, rather, a “collection of SCFTs” as we refer to it in the paper — for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M₃ and, secondly, is not limited to a particular supersymmetric partition function of T [M₃]. In particular, we propose to describe such “collection of SCFTs” in terms of 3d N = 2 gauge theories with “non-linear matter” fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [M₃], and propose new tools to compute more recent q-series invariants Ẑ (M₃) in the case of manifolds with b₁ > 0. Although we use genus-1 mapping tori as our “case study,” many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.

Item Type:Article
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URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Park, Sunghyuk0000-0002-6132-0871
Additional Information:© 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: June 29, 2020. Accepted: August 25, 2020. Published: September 23, 2020. Article funded by SCOAP3. It is pleasure to thank Ian Agol, Francesco Benini, Miranda Cheng, Francesca Ferrari, Michael Freedman, Sarah Harrison, Jeremy Lovejoy, Ciprian Manolescu, Satoshi Nawata, Du Pei, Pavel Putrov, Larry Rolen, Nathan Seiberg, Cumrun Vafa, and Christian Zickert for help and suggestions. The work of S.C. was supported by the US Department of Energy under grant DE-SC0010008. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of S.P. is supported by Kwanjeong Educational Foundation. N.S. gratefully acknowledges the support of the Dominic Orr Graduate Fellowship at Caltech.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0010008
Department of Energy (DOE)DE-SC0011632
Kwanjeong Educational FoundationUNSPECIFIED
Dominic Orr Graduate FellowshipUNSPECIFIED
Subject Keywords:Conformal Field Models in String Theory, Supersymmetric Effective Theories, Topological Field Theories
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Issue or Number:9
Record Number:CaltechAUTHORS:20200925-091915393
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Official Citation:Chun, S., Gukov, S., Park, S. et al. 3d-3d correspondence for mapping tori. J. High Energ. Phys. 2020, 152 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105543
Deposited By: George Porter
Deposited On:25 Sep 2020 16:56
Last Modified:16 Nov 2021 18:44

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