Gaillard-Zumino non-invertible symmetries

TL;DR

This paper discovers an infinite class of non-invertible zero-form symmetries in four-dimensional models related to Gaillard-Zumino, extending known symmetries to a larger quantum subgroup through topological defects.

Contribution

It introduces a new class of non-invertible symmetries in GZ models, explicitly constructs the associated defects, and explores their fusion rules and implications.

Findings

Non-invertible symmetries extend the classical GZ symmetries.

Explicit construction of topological defects and their fusion rules.

Examples include axion-dilaton-Maxwell and certain supergravity models.

Abstract

We uncover an infinite class of novel zero-form non-invertible symmetries in a broad family of four-dimensional models, studied years ago by Gaillard and Zumino (GZ), which includes several extended supergravities as particular subcases. The GZ models consist of abelian gauge fields coupled to a neutral sector, typically including a set of scalars, whose equations of motion are classically invariant under a continuous group $\mathscr{G}$ acting on the electric and magnetic field strengths via symplectic transformations. The standard lore holds that, at the quantum level, these symmetries are broken to an integral subgroup $\mathscr{G}_\mathbb{Z}$. We show that, in fact, a much larger subgroup $\mathscr{G}_\mathbb{Q}$ survives, albeit through non-invertible topological defects. We explicitly construct these defects and compute some of their fusion rules. As illustrative examples, we consider the axion-dilaton-Maxwell model and the bosonic sector of a class of $\mathcal{N}=2$ supergravities of the kind that appear in type II Calabi-Yau compactifications. Finally, we comment on how (part of) these non-invertible zero-form symmetries can be broken by gauging the $\mathscr{G}_\mathbb{Z}$ subgroup of invertible symmetries.