WZW orientifolds and finite group cohomology

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2008

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The simplest orientifolds of the WZW models are obtained by gauging a double script Z sign2symmetry 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 →(ζ 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 Γ = ℤ2 × Z that combine the ℤ2action 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 Γ = ℤ × Z. © 2008 Springer-Verlag.

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Quelldatensatz: oai:www.edit.fis.uni-hamburg.de:publications/28f939ca-ca66-4e03-a984-2840fc2ba632