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Orientifolds of the 3-sphere

Constantin Bachas·Nicolas Couchoud·Paul Windey
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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.

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Constantin Bachas, Nicolas Couchoud, Paul Windey. 2001-12-20. Orientifolds of the 3-sphere. https://doi.org/10.1088/1126-6708%2F2001%2F12%2F003

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