Dilogarithm Identities and Characters of Exceptional Rational Conformal Field Theories

Based on our recently published article Fermionic Expressions for the Characters of cp,1 Logarithmic Conformal Field Theories in the journal Nuclear Physics B, fermionic sum representations for the characters of the W(2, 2p−1, 2p−1, 2p−1) series of triplet algebras are obtained, providing further evidence that these logarithmic theories constitute well-defined rational conformal field theories. Furthermore, after an investigation of Nahm’s conjecture, fermionic character expressions for other conformal field theories such as the minimal Virasoro models and SU(2) Wess-Zumino-Witten (WZW) models are given, some of the latter also being new. In combination with their known bosonic counterparts, fermionic character expressions give rise to so-called bosonic-fermionic q-series identities, closely related to the famous Rogers-Ramanujan and Andrews-Gordon identities. Additionally, it is displayed how fermionic character expressions imply dilogarithm identities for the effective central charge of the conformal field theory in question. In the case of the triplet algebras, this results in an infinite series of dilogarithm identities. Since a proof for this series of identities already exists, this strongly supports the corresponding fermionic character expressions. In general, fermionic sum representations for characters give rise to an interpretation of the corresponding theory in terms of quasi-particles which obey generalized exclusion statistics. This quasi-particle content is discussed for conformal field theories which admit fermionic character expressions.