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T-Duality for Orientifolds and Twisted KR-Theory

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Charles Doran & Stefan Méndez-Diez

  2. Department of Mathematics, University of Maryland, College Park, MD, 20742-4015, USA

    Jonathan Rosenberg

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  1. Charles Doran
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  2. Stefan Méndez-Diez
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  3. Jonathan Rosenberg
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Correspondence to Jonathan Rosenberg.

Additional information

JR partially supported by NSF Grant DMS-1206159.

CD and SMD partially supported by the NSERC of Canada, the Pacific Institute for the Mathematical Sciences, and the McCalla Professorship at the University of Alberta.

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Doran, C., Méndez-Diez, S. & Rosenberg, J. T-Duality for Orientifolds and Twisted KR-Theory. Lett Math Phys 104, 1333–1364 (2014). https://doi.org/10.1007/s11005-014-0715-0

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