Towards higher super-$\sigma$-model categories

Abstract

A simplicial framework for the gerbe-theoretic modelling of supercharged-loop dynamics in the presence of worldsheet defects is discussed whose equivariantisation with respect to global supersymmetries of the bulk theory and subsequent orbit decomposition lead to a natural stratification of and cohomological superselection rules for target-space supergeometry, expected to encode essential information on the quantised 2$d$ field theory. A physically relevant example is analysed in considerable detail.

10 pages, to appear in the Proceedings of the 34th International Colloquium on Group Theoretical Methods in Physics, July 18-22 2022, Strasbourg