Gauge Defects

TL;DR

This paper explores gauge defects as non-invertible operators arising from gauging symmetries, focusing on their fusion properties in two-dimensional theories, and introduces a novel perspective on symmetry condensation as a $-1$-form symmetry.

Contribution

It introduces the concept of gauge defects as $-1$-form symmetries and analyzes their fusion in 2D theories, providing new insights into symmetry condensation and defect operators.

Findings

Gauge defects form a non-invertible fusion algebra.

Gauging symmetries can be viewed as condensation leading to $-1$-form symmetries.

The fusion properties of gauge defects are characterized in various 2D models.

Abstract

Gauging a symmetry can be thought of as the insertion of a spacetime-filling defect. Accordingly, we regard each gaugeable symmetry in a theory as defining a $-1$-form symmetry via condensation. The resulting operators, called gauge defects, have a natural fusion product, generally non-invertible, which we explore in a variety of two-dimensional theories.