Super-Higher-Form Symmetries

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 At the end we provide as an original unpublished contribution some hints on how to construct super-symTFT for Chern-Weil and geometric Chern-Weil symmetries directly from supergravity.