Real bundle gerbes, orientifolds and twisted KR-homology

Pedram Hekmati, Michael K. Murray, Richard J. Szabo, Raymond F. Vozzo

Research output: Contribution to journalArticle

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 languageEnglish
JournalAdvances in Theoretical and Mathematical Physics
Publication statusSubmitted - 2016

Keywords

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

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