Dilogarithm identities, fusion rules and structure constants of CFTs

Details Dilogarithm identities, fusion rules and structure constants of CFTs Dilogarithm identities, fusion rules and structure constants of CFTs

1993-07-08

arxiv.org/abs/hep-th/9307056v1

Mod.Phys.Lett. A9 (1994) 133-142

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1142/S0217732394000149

Recently dilogarithm identities have made their appearance in the physics literature. These identities seem to allow to calculate structure constants like, in particular, the effective central charge of certain conformal field theories from their fusion rules. In Nahm, Recknagel, Terhoeven (1992) a proof of identities of this type was given by considering the asymptotics of character functions in the so-called Rogers-Ramanujan sum form and comparing with the asymptotics predicted by modular covariance. Refining the argument, we obtain {\it the general connection of quantum dimensions of certain conformal field theories to the arguments of the dilogarithm function} in the identities in question and {\it an infinite set of consistency conditions on the parameters of Rogers-Ramanujan type partitions for them to be modular covariant}.

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