Notes on the Verlinde formula in non-rational conformal field theories
Abstract
We review and extend evidence for the validity of a generalized Verlinde formula in particular non-rational conformal field theories. We identify a subset of representations of the chiral algebra in non-rational conformal field theories that give rise to an analogue of the relation between modular S-matrices and fusion coefficients in rational conformal field theories. To that end we review and extend the Cardy-type brane calculations in bosonic and supersymmetric Liouville theory (and its duals) as well as in the hyperbolic three-plane H3+. We analyze the three-point functions of Liouville theory and of H3+ in detail to directly identify the fusion coefficients from the operator product expansion.
Keywords
Cite
@article{arxiv.hep-th/0601085,
title = {Notes on the Verlinde formula in non-rational conformal field theories},
author = {Charles Jego and Jan Troost},
journal= {arXiv preprint arXiv:hep-th/0601085},
year = {2008}
}
Comments
29 pages, 6 figures, v2: minor corrections, PRD version