Real bundle gerbes, orientifolds and twisted KR-homology
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.
Keywords
Cite
@article{arxiv.1608.06466,
title = {Real bundle gerbes, orientifolds and twisted KR-homology},
author = {Pedram Hekmati and Michael K. Murray and Richard J. Szabo and Raymond F. Vozzo},
journal= {arXiv preprint arXiv:1608.06466},
year = {2021}
}
Comments
44 pages; v2: minor changes, citations added; v3: technical corrections throughout, main results unchanged, some clarifying comments and reference added; v4: exposition improved, proof of Theorem 6.10 corrected, references added; v5: Final version to appear in Advances in Theoretical and Mathematical Physics; v6: published version with minor corrections, references updated