Notes on the Verlinde formula in nonrational conformal field theories
- Centre de Physique Theorique de l'Ecole Polytechnique 91128 Palaiseau Cedex (France)
- Laboratoire de Physique Theorique de l'Ecole Normale Superieure 24, Rue Lhomond 75231 Paris Cedex 05 (France)
We review and extend evidence for the validity of a generalized Verlinde formula, in particular, nonrational conformal field theories. We identify a subset of representations of the chiral algebra in nonrational 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 H{sub 3}{sup +}. We analyze the three-point functions of Liouville theory and of H{sub 3}{sup +} in detail to directly identify the fusion coefficients from the operator product expansion. Moreover, we check the validity of a proposed generic formula for localized brane one-point functions in nonrational conformal field theories.
- OSTI ID:
- 20864163
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 74, Issue 10; Other Information: DOI: 10.1103/PhysRevD.74.106002; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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