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arXiv · 1608.06466

Real bundle gerbes, orientifolds and twisted KR-homology

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

We consider Real bundle gerbes on manifolds equipped with an involution 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. Using these modules as building blocks, we introduce geometric cycles for twisted KR-homology and prove that they generate 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 model both refines and extends previous results by Wang and Baum-Carey-Wang to the Real setting. Our constructions further provide 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.

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Pedram Hekmati, Michael K. Murray, Richard J. Szabo, Raymond F. Vozzo. 2016-08-23. Real bundle gerbes, orientifolds and twisted KR-homology. https://doi.org/10.4310/atmp.2019.v23.n8.a5

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