Symmetry fractionalization and duality defects in Maxwell theory

TL;DR

This paper explores the structure of Maxwell theory on non-spin manifolds, revealing how different symmetry fractionalizations and duality defects lead to non-invertible symmetries, with implications for topological and gauge theories.

Contribution

It introduces gauging maps connecting non-anomalous Maxwell theories, constructs topological interfaces for SL(2,Z) duality, and develops duality defects resulting in non-invertible symmetries.

Findings

Identified three non-anomalous and one anomalous Maxwell theories with distinct symmetry fractionalizations.

Constructed topological interfaces associated with SL(2,Z) duality and one-form symmetry gauging.

Generated non-invertible symmetries through stacking duality defects.

Abstract

We consider Maxwell theory on a non-spin manifold. Depending on the choice of statistics for line operators, there are three non-anomalous theories and one anomalous theory with different symmetry fractionalizations. We establish the gauging maps that connect the non-anomalous theories by coupling them to a discrete gauge theory. We also construct topological interfaces associated with $\mathrm{SL}(2,\mathbb{Z})$ duality and gauging of electric and magnetic one-form symmetries. Finally, by stacking the topological interfaces, we compose various kinds of duality defects, which lead to non-invertible symmetries of non-spin Maxwell theories.