Orientifolds and K-theory

TL;DR

This paper introduces a new twisted equivariant Real K-theory framework to accurately describe D-brane spectra in orientifolds, extending previous models and aligning with BCFT results.

Contribution

It defines a novel twisted equivariant Real K-theory that classifies D-branes in orientifolds, incorporating generalised group cohomology and providing explicit calculations for specific orientifolds.

Findings

Established a twisted equivariant Real K-theory model for orientifolds.

Calculated the equivariant orthogonal K-theory for specific orientifolds.

Confirmed agreement between K-theory predictions and BCFT results.

Abstract

Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real K-theory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for such orientifolds. We find that equivariant Real K-theory can be twisted by elements of a generalised group cohomology. This cohomology classifies all orientifolds just as group cohomology classifies all orbifolds. As an example we consider the $\Omega\times\I_4$ orientifolds. We completely determine the equivariant orthogonal K-theory $KO_{\Zop_2}(\R^{p,q})$ and analyse the twisted versions. Agreement is found between K-theory and Boundary Confromal Field Theory (BCFT) results for both integrally- and torsion-charged D-branes.