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Authors
L.R. Huiszoon
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The simple current construction of orientifolds based on rational conformal field theories is reviewed. When applied to SO(16) level 1, one can describe all ten-dimensional orientifolds in a unified framework.
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The aim of this paper is to study orientifolds of c=1 conformal field theories. A systematic analysis of the allowed orientifold projections for c=1 orbifold conformal field theories is given. We compare the Klein bottle amplitudes obtained at rational points with the orientifold projections that we claim to be consistent for any value of the orbifold radius. We show that the recently obtained Klein bottle amplitudes corresponding to exceptional modular invariants, describing bosonic string theories at fractional square radius, are also in agreement with those orientifold projections.
We compute the prepotential for gauge theories descending from ${cal N}=4$ SYM via quiver projections and mass deformations. This accounts for gauge theories with product gauge groups and bifundamental matter. The case of massive orientifold gauge theories with gauge group SO/Sp is also described. In the case with no gravitational corrections the results are shown to be in agreement with Seiberg-Witten analysis and previous results in the literature.
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.
We study the relation between the dilaton action and sigma models for the Goldstone bosons of the spontaneous breaking of the conformal group. We argue that the relation requires that the sigma model is diffeomorphism invariant. The origin of the WZW terms for the dilaton is clarified and it is shown that in this approach the dilaton WZW term is necessarily accompanied by a Weyl invariant term proposed before from holographic considerations.
We discuss the holographic description of Narain $U(1)^ctimes U(1)^c$ conformal field theories, and their potential similarity to conventional weakly coupled gravity in the bulk, in the sense that the effective IR bulk description includes $U(1)$ gravity amended with additional light degrees of freedom. Starting from this picture, we formulate the hypothesis that in the large central charge limit the density of states of any Narain theory is bounded by below by the density of states of $U(1)$ gravity. This immediately implies that the maximal value of the spectral gap for primary fields is $Delta_1=c/(2pi e)$. To test the self-consistency of this proposal, we study its implications using chiral lattice CFTs and CFTs based on quantum stabilizer codes. First we notice that the conjecture yields a new bound on quantum stabilizer codes, which is compatible with previously known bounds in the literature. We proceed to discuss the variance of the density of states, which for consistency must be vanishingly small in the large-$c$ limit. We consider ensembles of code and chiral theories and show that in both cases the density variance is exponentially small in the central charge.
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