Real bundle gerbes, orientifolds and twisted KR-homology

Autor(es)

Hekmati, Pedram ^[1] ; Murray, Michael K. ^[2] ; Szabo, Richard J. ^{[3, 4, 5]} ; Vozzo, Raymond F. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Auckland, Dept Math, Auckland 1010 - New Zealand

^[2] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005 - Australia

^[3] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Santo Andre, SP - Brazil

^[4] Heriot Watt Univ, Dept Math, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian - Scotland

^[5] Heriot Watt Univ, Higgs Ctr Theoret Phys, Edinburgh EH14 4AS, Midlothian - Scotland

• Tipo de documento: Artigo Científico
• Fonte: Advances in Theoretical and Mathematical Physics; v. 23, n. 8, p. 2093-2159, 2019.
• Citações Web of Science: 0

Resumo

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 {[}55] and Baum-Carey-Wang {[}9] 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. (AU)

• Processo FAPESP: 16/04341-5 - Os aspectos clássicos e quânticos das teorias de campo nos espaços não-geométricos
• Beneficiário: Vladislav Kupriyanov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional