### Abstract

We introduce a notion of Real bundle gerbes on manifolds equipped with an involution. We elucidate their relation to Jandl gerbes and prove that they are classified by their Real Dixmier-Douady class in Grothendieck's equivariant sheaf cohomology. We show that the Grothendieck group of Real bundle gerbe modules is isomorphic to twisted KR-theory for a torsion Real Dixmier-Douady class. Building on the Baum-Douglas model for K-homology and the orientifold construction in string theory, we introduce geometric cycles for twisted KR-homology groups using Real bundle gerbe modules. We prove that this defines a real-oriented generalised homology theory dual to twisted KR-theory for Real closed manifolds, and more generally for Real finite CW-complexes, for any Real Dixmier-Douady class. This is achieved by defining an explicit natural transformation to analytic twisted KR-homology and proving that it is an isomorphism. Our constructions give a new framework for the classification of orientifolds in string theory, providing precise conditions for orientifold lifts of H-fluxes and for orientifold projections of open string states.

Original language | English |
---|---|

Journal | Advances in Theoretical and Mathematical Physics |

Publication status | Submitted - 2016 |

### Keywords

- hep-th
- math-ph
- math.DG
- math.KT
- math.MP

## Fingerprint Dive into the research topics of 'Real bundle gerbes, orientifolds and twisted KR-homology'. Together they form a unique fingerprint.

## Cite this

Hekmati, P., Murray, M. K., Szabo, R. J., & Vozzo, R. F. (2016). Real bundle gerbes, orientifolds and twisted KR-homology. Manuscript submitted for publication.