Chern-Simons theory, decomposition, and the A model

TL;DR

This paper explores how gauging one-form symmetries in Chern-Simons theories can be understood through an A-twisted topological string framework, revealing a worldsheet perspective on decomposition and higher-form symmetries.

Contribution

It provides a novel worldsheet description of gauged Chern-Simons theories with one-form symmetries, connecting target-space constraints to worldsheet realizations and illustrating the decomposition phenomenon.

Findings

Worldsheet models for gauged Chern-Simons theories are constructed.

A correspondence between worldsheet and target-space higher-form symmetries is demonstrated.

The decomposition of theories with one-form symmetry gauging is explicitly described.

Abstract

In this paper, we discuss how gauging one-form symmetries in Chern-Simons theories is implemented in an A-twisted topological open string theory. For example, the contribution from a fixed H/Z bundle on a three-manifold M, arising in a BZ gauging of H Chern-Simons, for Z a finite subgroup of the center of H, is described by an open string worldsheet theory whose bulk is a sigma model with target a Z-gerbe (a bundle of one-form symmetries) over T^* M, of characteristic class determined by the H/Z bundle. We give a worldsheet picture of the decomposition of one-form-symmetry-gauged Chern-Simons in three dimensinos, and we describe how a target-space constraint on bundles arising in the gauged Chern-Simons theory has a natural worldsheet realization. Our proposal provides examples of the expected correspondence between worldsheet global higher-form symmetries, and target-space gauged higher-form symmetries.