Geometry of WZW Orientifolds

Details Geometry of WZW Orientifolds Geometry of WZW Orientifolds

2001-10-29

arxiv.org/abs/hep-th/0110267v3

Nucl.Phys. B624 (2002) 219-252

Physics

High Energy Physics

High Energy Physics - Theory

35 pages LaTeX, 2 tables; Proof added for symmetric space relation; minor improvements; references added

Scientific paper

10.1016/S0550-3213(02)00005-6

We analyze unoriented Wess-Zumino-Witten models from a geometrical point of view. We show that the geometric interpretation of simple current crosscap states is as centre orientifold planes localized on conjugacy classes of the group manifold. We determine the locations and dimensions of these planes for arbitrary simply-connected groups and orbifolds thereof. The dimensions of the O-planes turn out to be given by the dimensions of symmetric coset manifolds based on regular embeddings. Furthermore, we give a geometrical interpretation of boundary conjugation in open unoriented WZW models; it yields D-branes together with their images under the orientifold projection. To find the agreement between O-planes and crosscap states, we find explicit answers for lattice extensions of Gaussian sums. These results allow us to express the modular P-matrix, which is directly related to the crosscap coefficient, in terms of characters of the horizontal subgroup of the affine Lie algebra. A corollary of this relation is that there exists a formal linear relation between the modular P- and the modular S-matrix.

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