Gaillard-Zumino non-invertible symmetries

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 $\mathcal{G}$ 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 ${\mathcal{G}}_{\mathbb{Z}}$. We show that, in fact, a much larger subgroup ${\mathcal{G}}_{\mathbb{Q}}$ 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 ${\mathcal{G}}_{\mathbb{Z}}$ subgroup of invertible symmetries.

50 pages + appendices, 3 figures, v2 fixed typos, references added, v3 published version