Super-Higher-Form Symmetries

TL;DR

This paper explores higher-form symmetries in supersymmetric theories using supergeometry, revealing new topological supercurrents and constructing related operators and defects.

Contribution

It introduces a supergeometry framework to construct and analyze higher-form symmetries, including Chern-Weil and geometric Chern-Weil symmetries, in supersymmetric theories.

Findings

Identified enlarged sets of topological conserved supercurrents.

Constructed operators and charged defects in N=1 super-Maxwell theory.

Provided initial ideas for super-symTFT construction from supergravity.

Abstract

We review the construction of higher-form symmetries for supersymmetric theories using a supergeometry framework. This reveals an enlarged set of topological conserved supercurrents, including Chern-Weil symmetries and new geometric Chern-Weil symmetries built from invariant supermanifold forms. In N=1 super-Maxwell theory in three dimensions, we construct the corresponding operators and charged defects, with charges determined by a super-linking number between their supporting hypersurfaces. At the end we provide as an original unpublished contribution some hints on how to construct super-symTFT for Chern-Weil and geometric Chern-Weil symmetries directly from supergravity.