Letters in Mathematical Physics

, Volume 104, Issue 11, pp 1333–1364 | Cite as

T-Duality for Orientifolds and Twisted KR-Theory

  • Charles Doran
  • Stefan Méndez-Diez
  • Jonathan RosenbergEmail author


D-brane charges in orientifold string theories are classified by the KR-theory of Atiyah. However, this is assuming that all O-planes have the same sign. When there are O-planes of different signs, physics demands a “KR-theory with a sign choice” which up until now has not been studied by mathematicians (with the unique exception of Moutuou, who did not have a specific application in mind). We give a definition of this theory and compute it for orientifold theories compactified on S 1 and T 2. We also explain how and why additional “twisting” is implemented. We show that our results satisfy all possible T-duality relationships for orientifold string theories on elliptic curves, which will be studied further in subsequent work.


orientifold O-plane KR-theory T-duality Chan–Paton bundle brane charge 

Mathematics Subject Classification

Primary 19L50 Secondary 19L47 81T30 19L64 19M05 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Charles Doran
    • 1
  • Stefan Méndez-Diez
    • 1
  • Jonathan Rosenberg
    • 2
    Email author
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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