# Orientifolds and K-theory

Braun, V. and Stefanski, B. (2002). Orientifolds and K-theory. Paper presented at the NATO Advanced Study Institute on Progress in String Theory and M-Theory, 24-05-1999 - 05-06-1999, Cargese, France.

## 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.

Publication Type: Conference or Workshop Item (Paper) The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-010-0211-0_16 Q Science > QA MathematicsQ Science > QC Physics School of Mathematics, Computer Science & Engineering > Mathematics https://openaccess.city.ac.uk/id/eprint/12559
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