Kaluza-Klein Branes

TL;DR

This paper explores Kaluza-Klein branes as stationary submanifolds under circle actions, deriving cohomological equations and applying findings to string theory branes and magnetic monopole scenarios.

Contribution

It provides a detailed geometric and cohomological analysis of Kaluza-Klein branes, linking them to string theory objects and flux backgrounds, with explicit examples.

Findings

Branes correspond to stationary submanifolds under circle actions.

Derived cohomological equations for brane charge conditions.

Applied results to monopole-antimonopole production in 5D theories.

Abstract

We examine Kaluza-Klein branes in detail. Specifically, we show that codimension four submanifolds that are stationary under a semi-free circle action may be interpreted as branes or antibranes in the Kaluza-Klein reduced space that are magnetically charged under the Kaluza-Klein field strength. We derive the equation in cohomology that is satisfied by such a brane using an explicit construction of the Thom class of the normal bundle of the brane worldvolume in the reduced space. This may be applied to both the D6-brane of Type IIA String Theory, and also to various recent constructions of magnetic branes immersed in fluxbrane backgrounds. We then go on to study the special case of monopole-antimonopole production in a five-dimensional Kaluza-Klein theory, illustrating our arguments with various concrete examples.