Fabio Apruzzi (University of Padova)

Gaillard-Zumino non-invertible symmetries

In this talk I will discuss an infinite class of novel zero-form non-invertible symmetries in a broad family of four-dimensional field theoretical models, studied years ago by Gaillard and Zumino (GZ). 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 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. I will show how the subset of rational transformations survives, albeit through non-invertible topological defects. As illustrative example, I will first present the axion-dilaton-Maxwell model. Then I will illustrate the main aspects of the non-invertible GZ symmetries in the bosonic sector of certain supergravities, of the kind that appear in type II Calabi-Yau compactifications. Finally, I will comment on some implications of the gauging of the invertible integral subgroup.