Symmetry TFTs from String Theory

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

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