Symmetry TFTs from String Theory

TL;DR

This paper constructs a topological field theory, called SymTFT, from M-theory compactifications to encode higher-form symmetries and anomalies in various quantum field theories, using differential cohomology and brane web techniques.

Contribution

It introduces a novel framework for deriving SymTFTs from M-theory compactifications, incorporating torsion in cohomology and applying to both Lagrangian and non-Lagrangian theories.

Findings

Derived SymTFTs for 7d super-Yang Mills and 5d SCFTs.

Unified M-theory and IIB brane web approaches to symmetry analysis.

Framework accommodates torsion and non-Lagrangian theories.

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 $\partial X$ 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 $\partial X$, 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 $X= \mathbb{C}^2/\Gamma_{ADE}$, 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.