Bundle Gerbes and Surface Holonomy

TL;DR

This paper develops a systematic framework for Hermitian bundle gerbes with connection, extending surface holonomy concepts to unoriented surfaces, surfaces with boundaries, and defect lines, inspired by conformal field theory structures.

Contribution

It introduces a comprehensive geometric approach to bundle gerbes, including new structures like Jandl gerbes, D-branes, and bi-branes for broader surface types.

Findings

Defined surface holonomy for various surface types.

Extended bundle gerbe theory to unoriented and bordered surfaces.

Connected geometric structures to conformal field theory concepts.

Abstract

Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes under descent. Inspired by structures arising in a representation theoretic approach to rational conformal field theories, we introduce geometric structure that is appropriate to define surface holonomy in more general situations: Jandl gerbes for unoriented surfaces, D-branes for surfaces with boundaries, and bi-branes for surfaces with defect lines.