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Dilogarithm identities for conformal field theories and cluster algebras: simply laced case. (English) Zbl 1284.81157
Summary: The dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have been partly proved by various authors. We prove these identities in full generality for any pair of Dynkin diagrams of simply laced type based on the cluster algebra formulation of the Y-systems.

MSC:
81R12 Groups and algebras in quantum theory and relations with integrable systems
33B30 Higher logarithm functions
13F60 Cluster algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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