On Gauging Finite Symmetries by Higher Gauging Condensation Defects

TL;DR

This paper introduces a Lagrangian-based method to gauge finite 0-form symmetries in Dijkgraaf-Witten theories using higher gauging condensation defects, revealing their limitations and connections to higher group symmetries.

Contribution

It proposes a new EFT-style procedure for higher gauging of finite symmetries in Dijkgraaf-Witten theories and constructs explicit effective actions with detailed symmetry data.

Findings

Effective actions match expected discrete gauge theory properties

Braiding and fusion data align with theoretical predictions

Clarifies relations between symmetries and higher group structures

Abstract

Based on the work by C{\'o}rdova-Costa-Hsin (arXiv:2412.16681), we propose an EFT-style, Lagrangian procedure to gauge finite 0-form symmetries in untwisted Dijkgraaf-Witten gauge theories on closed oriented manifolds using higher gauging condensation defects and point out its limitations. Using this proposal, we construct effective actions of untwisted Dijkgraaf-Witten theories with Heisenberg gauge group over $\mathbb{Z}_p$ and show that the braiding data from Hopf link and the fusion rules match with the expected discrete gauge theories. We also study the symTFT implications of these effective Lagrangians and clarify their relations with higher group global symmetries.