Flat equivariant gerbes: holonomies and dualities

TL;DR

This paper explores how global topological data, such as holonomies of flat gauge fields, influence string compactifications and reveal dualities between different string backgrounds.

Contribution

It introduces a framework for understanding the role of flat gerbes and holonomies in string dualities, extending to broader classes of compactifications.

Findings

Holonomy choices affect string dualities.

Explicit examples demonstrate duality relations.

Implications for perturbative and non-perturbative string theory.

Abstract

We examine the role of global topological data associated to choices of holonomy for flat gauge fields in string compactification. Our study begins with perturbative string compactification on compact flat manifolds preserving 8 supercharges in 5 dimensions. By including non-trivial holonomy for Wilson lines in the heterotic string and for the B-field gerbe in the type II string we find worldsheet dualities that relate these backgrounds to other string compactifications. While our simple examples allow for explicit analysis, the concepts and some of the methods extend to a broader class of compactifications and have implications for string dualities, perturbative and otherwise.