# Orientifolds of the 3-sphere

Abstract : We study the geometry of orientifolds in the SU(2) WZW model. They correspond to the two inequivalent, orientation-reversing involutions of $S^3$, whose fixed-point sets are: the north and south poles (O0), or the equator two-sphere (O2). We show how the geometric action of these involutions leads unambiguously to the previously obtained algebraic results for the Klein bottle and Moebius amplitudes. We give a semiclassical derivation of the selection rules and signs in the crosscap couplings, paying particular attention to discrete B-fluxes. A novel observation, which does not follow from consistency of the one-loop vacuum diagrams, is that in the case of the O0 orientifolds only integer- or only half-integer-spin Cardy states may coexist.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-02301312
Contributor : Constantin Bachas <>
Submitted on : Monday, September 30, 2019 - 12:52:36 PM
Last modification on : Tuesday, October 15, 2019 - 4:42:55 PM

### Citation

Constantin Bachas, Nicolas Couchoud, Paul Windey. Orientifolds of the 3-sphere. Journal of High Energy Physics, Springer, 2001, 2001 (12), pp.003-003. ⟨10.1088/1126-6708/2001/12/003⟩. ⟨hal-02301312⟩

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