WZW orientifolds and finite group cohomology

Abstract

The simplest orientifolds of the WZW models are obtained by gauging a 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 (ζg)^{-1}, where ζis 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 hep-th/0512283. More generally, one may gauge orientifold symmetry groups Γ= Z_2 \ltimes Z that combine the 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-Γcohomology that we solve for all simple simply-connected compact Lie groups G and all orientifold groups Γ= Z_2 \ltimes Z.

48+1 pages, 11 figures

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Cited by in corpus (9)

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• Global gauge anomalies in two-dimensional bosonic sigma models
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• Decomposition in Chern-Simons theories in three dimensions
• The gauging of two-dimensional bosonic sigma models on world-sheets with defects
• Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects
• 2d Fu-Kane-Mele invariant as Wess-Zumino action of the sewing matrix
• Affine su(2) fusion rules from gerbe 2-isomorphisms
• Quasi-quantum groups from Kalb-Ramond fields and magnetic amplitudes for strings on orbifolds