Type I D-branes in an H-flux and twisted KO-theory

TL;DR

This paper explores the mathematical framework of twisted KO-theory for Type I D-branes in H-flux backgrounds, introducing real bundle gerbe KO-theory as a geometric realization and examining its relations and examples.

Contribution

It introduces real bundle gerbe KO-theory as a geometric model for twisted KO-theory, extending the understanding of D-brane charges in H-flux environments.

Findings

Real bundle gerbe KO-theory models twisted KO-theory geometrically.

Established relations between twisted KO-theory, K-theory, and Chern character.

Provided examples illustrating the theory and discussed open problems.

Abstract

Witten has argued that charges of Type I D-branes in the presence of an H-flux, take values in twisted KO-theory. We begin with the study of real bundle gerbes and their holonomy. We then introduce the notion of real bundle gerbe KO-theory which we establish is a geometric realization of twisted KO-theory. We examine the relation with twisted K-theory, the Chern character and provide some examples. We conclude with some open problems.