U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures

TL;DR

This paper investigates the interplay of higher-group and non-invertible symmetries in quantum field theories, especially in four and five dimensions, using symmetry TQFTs and analyzing models with mixed anomalies.

Contribution

It introduces a new framework for understanding intertwined higher symmetries via symmetry TQFTs in higher dimensions, with detailed analysis of boundary conditions and dressing choices.

Findings

Identifies a novel interplay between higher-group and non-invertible symmetries in 4D models.

Demonstrates the emergence of these structures in both gapless and gapped phases.

Extends the analysis to a 5D model with intrinsic symmetry structures.

Abstract

Quantum field theories can exhibit various generalized symmetry structures, among which higher-group symmetries and non-invertible symmetry defects are particularly prominent. In this work, we explore a new general scenario in which these two structures are intertwined. This phenomenon arises in four dimensions when gauging one of multiple $U(1)$ 0-form symmetries in the presence of mixed 't Hooft anomalies. We illustrate this with two distinct models that flow to an IR gapless phase and a gapped phase, respectively, and examine how this symmetry structure manifests in each case. Additionally, we investigate a five-dimensional model where a similar structure exists intrinsically. Our main tool is a symmetry TQFT in one higher dimension, formulated using non-compact gauge fields and having infinitely many topological operators. We carefully determine its boundary conditions and provide a detailed discussion on various dressing choices for its bulk topological operators.