Rigid models for 2-gerbes I: Chern-Simons geometry

TL;DR

This paper introduces a rigid model for bundle 2-gerbes with connective structures, simplifying explicit calculations for applications in physics and providing a new perspective on geometric string structures.

Contribution

It presents a novel rigid model for bundle 2-gerbes with connections, facilitating explicit calculations and connecting to existing Chern-Simons bundle 2-gerbes.

Findings

Rigid model for bundle 2-gerbes with connective structures

Construction of functorial correspondence to existing models

Application to geometric string structures and Chern-Simons theory

Abstract

Motivated by the problem of constructing explicit geometric string structures, we give a rigid model for bundle 2-gerbes, and define connective structures thereon. This model is designed to make explicit calculations easier in applications to physics. To compare to the existing definition, we give a functorial construction of a bundle 2-gerbe as in the literature from our rigid model, including with connections. As an example we prove that the Chern--Simons bundle 2-gerbe from the literature, with its connective structure, can be rigidified -- it arises, up to isomorphism in the strongest possible sense, from a rigid bundle 2-gerbe with connective structure via this construction. Further, our rigid version of 2-gerbe trivialisation (with connections) gives rise to trivialisations (with connections) of bundle 2-gerbes in the usual sense, and as such can be used to describe geometric string structures.