2007/01/09 by Krzysztof Gawędzki, Krzysztof Gawedzki, Rafał R. Suszek +2 · 12 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cohomology #Congruence subgroup #Homotopy and Cohomology in Algebraic Topology #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Orientifold #Physics #Pure mathematics #String field theory #String theory #Supersymmetry #Worldsheet #hep-th #math.DG
paper · pdf · doi:10.1007/s00220-008-0525-2
published in Communications in Mathematical Physics 284(1), 1-49 (Springer Science+Business Media) · 48+1 pages, 11 figures
arxiv created 2007/01/09 · openalex publication_date 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The simplest orientifolds of the WZW models are obtained by gauging a Z2 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 ↦ (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= Z2 \ltimes Z that combine the Z2-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= Z2 \ltimes Z.