Undoing decomposition

TL;DR

This paper explores how gauging one-form symmetries in two-dimensional theories can selectively undo the decomposition into disjoint sectors, providing explicit examples and uncovering hidden symmetries.

Contribution

It introduces a method to gauge one-form symmetries to select specific components of the disjoint union in 2D theories, with detailed examples and new insights into topological configurations.

Findings

Gauging one-form symmetries can undo decomposition in 2D theories.

Explicit analysis of orbifolds, Yang-Mills, and supersymmetric gauge theories.

Discovery of hidden one-form symmetries.

Abstract

In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition -- an issue resolved by the observation that such theories decompose into disjoint unions, a result that has been applied to, for example, Gromov-Witten theory and gauged linear sigma model phases. In this paper we describe how gauging one-form symmetries in two-dimensional theories can be used to select particular elements of that disjoint union, effectively undoing decomposition. We examine such gaugings explicitly in examples involving orbifolds, nonsupersymmetric pure Yang-Mills theories, and supersymmetric gauge theories in two dimensions. Along the way, we learn explicit concrete details of the topological configurations that path integrals sum over when gauging a one-form symmetry, and we also uncover `hidden' one-form symmetries.