Undoing decomposition

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.