On duality and extended chiral symmetry in the SL(2,R) WZW model

Two chiral aspects of the SL(2,R) WZW model in an operator formalism are investigated. First, the meaning of duality, or conjugation, of primary fields is clarified. On a class of modules obtained from the discrete series it is shown, by looking at spaces of two-point conformal blocks, that a natural definition of contragredient module provides a suitable notion of conjugation of primary fields, consistent with known two-point functions. We find strong indications that an apparent contradiction with the Clebsch-Gordan series of SL(2,R), and proposed fusion rules, is explained by nonsemisimplicity of a certain category. Second, results indicating an infinite cyclic simple current group, corresponding to spectral flow automorphisms, are presented. In particular, the subgroup corresponding to even spectral flow provides part of a hypothetical extended chiral algebra resulting in proposed modular invariant bulk spectra.Comment: 36 page

The Poincare mass operator in terms of a hyperbolic algebra

The Poincare mass operator can be represented in terms of a Cl(3,0) Clifford algebra. With this representation the quadratic Dirac equation and the Maxwell equations can be derived from the same mathematical structure.Comment: 5 pages Latex2

Uniqueness of open/closed rational CFT with given algebra of open states

We study the sewing constraints for rational two-dimensional conformal field theory on oriented surfaces with possibly non-empty boundary. The boundary condition is taken to be the same on all segments of the boundary. The following uniqueness result is established: For a solution to the sewing constraints with nondegenerate closed state vacuum and nondegenerate two-point correlators of boundary fields on the disk and of bulk fields on the sphere, up to equivalence all correlators are uniquely determined by the one-, two,- and three-point correlators on the disk. Thus for any such theory every consistent collection of correlators can be obtained by the TFT approach of hep-th/0204148, hep-th/0503194. As morphisms of the category of world sheets we include not only homeomorphisms, but also sewings; interpreting the correlators as a natural transformation then encodes covariance both under homeomorphisms and under sewings of world sheets.Comment: 77 pages, several figures; v2: minor corrections, version published in ATM

Partition functions, mapping class groups and Drinfeld doubles

Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete expressions obtained for the case of Drinfeld doubles of finite groups. The results for doubles are independent of the characteristic of the underlying field, and the general results do not require any assumptions of semisimplicity.Comment: Slightly extended version of contribution to the Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics (Tianjin, August 2012). v2: typos correcte

CFT description of three-dimensional Kerr-de Sitter spacetime

We describe three-dimensional Kerr-de Sitter space using similar methods as recently applied to the BTZ black hole. A rigorous form of the classical connection between gravity in three dimensions and two-dimensional conformal field theory is employed, where the fundamental degrees of freedom are described in terms of two dependent SL(2,C) currents. In contrast to the BTZ case, however, quantization does not give the Bekenstein-Hawking entropy connected to the cosmological horizon of Kerr-de Sitter space.Comment: 12 pages, v2: references added and some structural change

A no-ghost theorem for the bosonic Nappi-Witten string

We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten spacetime. This is achieved in two steps. We first demonstrate unitarity for a class of NW/U(1) modules: the norm of any state which is primary with respect to a chosen timelike U(1) is non-negative. We then show that physical states - states satisfying the Virasoro constraints - in a class of modules of an affinisation of the Nappi-Witten algebra are contained in the NW/U(1) modules. Similar to the case of strings on $AdS_3$, in order to saturate the spectrum obtained in light-cone quantization we are led to include modules with energy not bounded from below, which are related to modules with energy bounded from below by spectral flow automorphisms.Comment: 24 pages, 1 figur