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Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups

Gukov, Sergei and Pei, Du and Reid, Charles and Shehper, Ali (2021) Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20211206-191012374

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Abstract

We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose fusion rules can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act by phases. This leads to an explicit description of the gauging of these symmetries. One application of our results is a generalization of the equivariant Verlinde formula to the case of general Lie groups. The generalized formula leads to many predictions for the geometry of Hitchin moduli spaces, which we explicitly check in several cases with low genus and SO(3) gauge group.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2111.08032PublisherDiscussion Paper
ORCID:
AuthorORCID
Gukov, Sergei0000-0002-9486-1762
Pei, Du0000-0001-5587-6905
Reid, Charles0000-0003-4598-5635
Shehper, Ali0000-0002-3440-1721
Additional Information:We would like to thank Dan Freed, Po-Shen Hsin, Andrew Neitzke, and Sebastian Schulz for useful discussions. We would also like to thank Simons Center for Geometry and Physics for generous hospitality during Graduate Summer School on the Mathematics and Physics of Hitchin Systems and the Simons Summer Workshop 2021. The work of SG 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 1664227. The work of AS was supported by NSF grants DMS-2005312 and DMS1711692. The work of DP was supported by the Center for Mathematical Sciences and Application. This paper is partly a result of the ERC-SyG project, Recursive and Exact New Quantum Theory (ReNewQuantum) which received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 810573.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
NSFDMS-1664227
NSFDMS-2005312
NSFDMS-1711692
European Research Council (ERC)810573
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2021-041
Record Number:CaltechAUTHORS:20211206-191012374
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20211206-191012374
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112233
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:07 Dec 2021 17:44
Last Modified:07 Dec 2021 17:44

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