The Branes Behind Generalized Symmetry Operators

TL;DR

This paper explores how branes in string theory give rise to generalized symmetry operators in quantum field theories, revealing their properties and fusion rules, especially in 6D superconformal theories via F-theory.

Contribution

It systematically connects brane configurations to topological symmetry operators and their fusion rules in QFTs, providing a geometric framework for understanding these symmetries.

Findings

Branes wrapped on cycles correspond to topological symmetry operators.

Worldvolume theories of these operators can be derived from string constructions.

Non-invertible fusion rules are identified for certain defects in 6D SCFTs.

Abstract

The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry $X$, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary $\partial X$. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in $\partial X$. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.