Holonomies of Intersecting Branes

TL;DR

This paper explores the geometric and topological properties of gauge fields in string and M-theory, focusing on how certain structures impose conditions on fluxes via Deligne cohomology.

Contribution

It introduces a framework linking string structures and flux conditions through the use of relative Deligne cohomology in the context of intersecting branes.

Findings

String structure leads to specific topological flux conditions.

Deligne cohomology effectively describes gauge field geometry.

Topological constraints are derived for five-brane configurations.

Abstract

We discuss the geometry of string and M-theory gauge fields in Deligne cohomology. In particular, we show how requiring string structure (or loop space Spin-C structure) on the five-brane leads to topological conditions on the flux in the relative Deligne cohomology of the bulk - brain pair.