Unoriented WZW Models and Holonomy of Bundle Gerbes

TL;DR

This paper extends the concept of surface holonomy of bundle gerbes to unoriented surfaces, providing a geometric framework for the Wess-Zumino term in unoriented WZW models, aligning with algebraic results.

Contribution

It introduces a new structure for bundle gerbes enabling surface holonomy on unoriented surfaces, advancing the geometric understanding of WZW models.

Findings

Reproduces algebraic results for unoriented WZW models

Defines a new structure for bundle gerbes

Extends surface holonomy to unoriented surfaces

Abstract

The Wess-Zumino term in two-dimensional conformal field theory is best understood as a surface holonomy of a bundle gerbe. We define additional structure for a bundle gerbe that allows to extend the notion of surface holonomy to unoriented surfaces. This provides a candidate for the Wess-Zumino term for WZW models on unoriented surfaces. Our ansatz reproduces some results known from the algebraic approach to WZW models.