The Higher Structure of Symmetries of Axion-Maxwell Theory

TL;DR

This paper explores the complex symmetry structures in Axion-Maxwell theory, focusing on topological defects and their higher categorical organization, and explicitly computes certain algebraic invariants related to non-invertible symmetries.

Contribution

It provides a detailed analysis of the higher categorical structure of generalized symmetries in Axion-Maxwell theory, including explicit calculations of F-symbols for non-invertible symmetries.

Findings

Explicit computation of generalized F-symbols for non-invertible electric 1-form symmetry.

Clarification of the worldvolume approach to defect calculus.

Enhanced understanding of the higher categorical structure of symmetries.

Abstract

Generalized symmetries of quantum field theories can be characterized by topological defects/operators organized into a higher category. In this paper we consider the Axion-Maxwell field theory in four dimensions and, building on the construction of its topological defects by Choi, Lam, Shao, Hidaka, Nitta and Yokokura, we discuss field theoretical methods to compute some aspects of the higher structure of such category. In particular, we determine explicitly the generalized F-symbols for the non-invertible electric 1-form symmetry of the theory. Along the way, we clarify various aspects of the bottom-up worldvolume approach towards the calculus of defects.