Half-Spacetime Gauging of 2-Group Symmetry in 3d

TL;DR

This paper introduces a novel method of half-spacetime gauging of 2-group symmetries in 3d quantum field theories, leading to non-invertible duality defects with explicit fusion rules.

Contribution

It constructs and analyzes non-invertible duality defects arising from half-spacetime gauging of 2-group symmetries, with detailed examples and fusion rule derivations.

Findings

Gauging one symmetry factor yields a theory with a 2-group symmetry.

Gauging another factor produces a non-invertible 0-form symmetry.

Explicit fusion rules for the non-invertible defects are derived.

Abstract

We construct a class of non-invertible duality defects, in (2+1)d quantum field theories, arising from half-spacetime gauging of a 2-group symmetry. Starting from a parent theory with two discrete and Abelian 0-form symmetries and a prescribed mixed anomaly, we show that gauging one factor produces a theory with a 2-group symmetry, while gauging the other yields a theory with a non-invertible 0-form symmetry, whose fusion rules we derive explicitly. When the parent theory possesses three such symmetries with a cyclic anomaly structure, gauging different factors can produce mutually dual theories and the half-spacetime gauging of the 2-group is implemented by a non-invertible duality defect, whose fusion rules we obtain. We illustrate the construction with explicit examples, including a $U(1)\times U(1)\times U(1)$ gauge theory and a general class of product theories. We also include a self-contained pedagogical introduction to the cohomological tools employed throughout the article.