Dilogarithm identities, fusion rules and structure constants of CFTs

Abstract

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}.

11 pages

Cited by in corpus (8)

• Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
• Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
• Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4ν)
• Multinomials and Polynomial Bosonic Forms for the Branching Functions of the $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$ Conformal Coset Models
• Polynomial Fermionic Forms for the Branching Functions of the Rational Coset Conformal Field Theories $\widehat{su}(2{)}_M\times \widehat{su}(2{)}_N/\widehat{su}(2{)}_{M+N}$}
• Central Charge and the Andrews-Bailey Construction
• On the topological and crosscap entropies in non-oriented RCFTs
• Exponents Associated with $Y$-Systems and their Relationship with $q$-Series