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Communications in Mathematical Physics

, Volume 284, Issue 1, pp 1–49 | Cite as

WZW Orientifolds and Finite Group Cohomology

  • Krzysztof GawȩdzkiEmail author
  • Rafał R. Suszek
  • Konrad Waldorf
Article

Abstract

The simplest orientifolds of the WZW models are obtained by gauging a \({\mathbb{Z}_2}\) symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion \({g\mapsto(\zeta g)^{-1}}\), where ζ is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in [31]. More generally, one may gauge orientifold symmetry groups \({\Gamma=\mathbb{Z}_2\times Z}\) that combine the \({\mathbb{Z}_2}\)-action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to a problem in group-Γ cohomology that we solve for all simple simply connected compact Lie groups G and all orientifold groups \({\Gamma=\mathbb{Z} _2\times Z}\).

Keywords

Cohomology Class Dynkin Diagram Equivariant Structure Feynman Amplitude Orbifold Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Krzysztof Gawȩdzki
    • 1
    Email author
  • Rafał R. Suszek
    • 2
  • Konrad Waldorf
    • 3
  1. 1.Laboratoire de PhysiqueENS-LyonLyonFrance
  2. 2.Department of MathematicsKing’s College London StrandLondonUK
  3. 3.Fachbereich MathematikUniversität HamburgHamburgGermany

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