Equivariant Cartan-Eilenberg supergerbes, the Kosteleck\'y-Rabin defect and descent to the Rabin-Crane superorbifold

TL;DR

This paper develops a geometric framework for super-p-brane models using higher-supergeometric structures, resolving topological issues via equivariant supergerbes and defining a new super-orbifold sigma-model.

Contribution

It introduces a concrete geometrisation scheme for Green-Schwarz cocycles, leading to higher-supergeometric structures with supersymmetry and equivariant properties on super-orbifolds.

Findings

Constructs higher-supergeometric supergerbes with supersymmetry

Shows equivariant structures resolve super-orbifold topology

Defines a novel super-p-brane sigma-model in the super-orbifold context

Abstract

A concrete geometrisation scheme is proposed for the Green-Schwarz cocycles in the supersymmetric de Rham cohomology of the super-minkowskian spacetime, which determine standard super-$\sigma$-model dynamics of super-p-branes. The scheme yields higher-supergeometric structures with supersymmetry akin to those known from the un-graded setting - distinguished (Murray-type) p-gerbe objects in the category of Lie supergroups. These are shown to carry a canonical equivariant structure for the action of the discrete Kosteleck\'y-Rabin subgroup of the target supersymmetry group on the target, and thus to resolve the `topology' of the corresponding Rabin-Crane soul superorbifold of the super-minkowskian spacetime. The equivariant structure is seen to effectively define a novel $\sigma$-model of super-p-brane dynamics in the super-orbifold through the construction of the corresponding (gauge-)symmetry defect.