Sign Choices for Orientifolds

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

Research output: Contribution to journalArticle

Abstract

We analyse the problem of assigning sign choices to O-planes in orientifolds of type II string theory. We show that there exists a sequence of invariant p-gerbes with p≥ - 1 , which give rise to sign choices and are related by coboundary maps. We prove that the sign choice homomorphisms stabilise with the dimension of the orientifold and we derive topological constraints on the possible sign configurations. Concrete calculations for spherical and toroidal orientifolds are carried out, and in particular we exhibit a four-dimensional orientifold where not every sign choice is geometrically attainable. We elucidate how the K-theory groups associated with invariant p-gerbes for p= - 1 , 0 , 1 interact with the coboundary maps. This allows us to interpret a notion of K-theory due to Gao and Hori as a special case of twisted KR-theory, which consequently implies the homotopy invariance and Fredholm module description of their construction.

Original languageEnglish
Pages (from-to)1843-1873
Number of pages31
JournalCommunications in Mathematical Physics
Volume378
Issue number3
Early online date18 Aug 2020
DOIs
Publication statusPublished - Sep 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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