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Symmetry TFTs from String Theory

Apruzzi, Fabio; Bonetti, Federico; García Etxebarria, Iñaki; Hosseini, Saghar S.; Schäfer-Nameki, Sakura

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Authors

Fabio Apruzzi

Sakura Schäfer-Nameki



Abstract

We determine the d+1 dimensional topological field theory, which encodes the higher-form symmetries and their ’t Hooft anomalies for d-dimensional QFTs obtained by compactifying M-theory on a non-compact space X. The resulting theory, which we call the Symmetry TFT, or SymTFT for short, is derived by reducing the topological sector of 11d supergravity on the boundary ∂X of the space X. Central to this endeavour is a reformulation of supergravity in terms of differential cohomology, which allows the inclusion of torsion in cohomology of the space ∂X, which in turn gives rise to the background fields for discrete (in particular higher-form) symmetries. We apply this framework to 7d super-Yang Mills, where X=C2/ΓADE, as well as the Sasaki–Einstein links of Calabi–Yau three-fold cones that give rise to 5d superconformal field theories. This M-theory analysis is complemented with a IIB 5-brane web approach, where we derive the SymTFTs from the asymptotics of the 5-brane webs. Our methods apply to both Lagrangian and non-Lagrangian theories, and allow for many generalisations.

Citation

Apruzzi, F., Bonetti, F., García Etxebarria, I., Hosseini, S. S., & Schäfer-Nameki, S. (2023). Symmetry TFTs from String Theory. Communications in Mathematical Physics, 402(1), 895-949. https://doi.org/10.1007/s00220-023-04737-2

Journal Article Type Article
Acceptance Date Apr 18, 2023
Online Publication Date May 26, 2023
Publication Date 2023-08
Deposit Date Aug 22, 2023
Publicly Available Date Aug 23, 2023
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 402
Issue 1
Pages 895-949
DOI https://doi.org/10.1007/s00220-023-04737-2
Public URL https://durham-repository.worktribe.com/output/1723452

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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