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arXiv · hep-th/0601085

Notes on the Verlinde formula in non-rational conformal field theories

Charles Jego·Jan Troost
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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.

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Charles Jego, Jan Troost. 2006-10-31. Notes on the Verlinde formula in non-rational conformal field theories. https://doi.org/10.1103/physrevd.74.106002

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