Twisted K-Theory from Monodromies

TL;DR

This paper explores how monodromies relate different RR fluxes within twisted K-theory, revealing their transformations and implications for flux classification, especially involving NS5-branes and noncompact spaces.

Contribution

It introduces the concept that monodromies connect fluxes in twisted K-theory, extending the understanding of flux classifications and their transformations under brane monodromies.

Findings

Monodromies relate different RR fluxes in twisted K-theory.

NS5-brane monodromies alter flux classifications.

In noncompact spaces, K-theory cannot distinguish certain flux configurations.

Abstract

RR fluxes representing different cohomology classes may correspond to the same twisted K-theory class. We argue that such fluxes are related by monodromies, generalizing and sometimes T-dual to the familiar monodromies of a D7-brane. A generalized theta angle is also transformed, but changes by a multiple of 2pi. As an application, NS5-brane monodromies modify the twisted K-theory classification of fluxes. Furthermore, in the noncompact case K-theory does not distinguish flux configurations in which dG is nontrivial in compactly supported cohomology. Such fluxes are realized as the decay products of unstable D-branes that wrapped nontrivial cycles. This is interpreted using the E8 bundle formalism.