| Résume | The dilogarithm identities for the central charges of conformal field theories were conjectured by Bazhanov, Kirillov , and Reshetikhin inthe late 80's. They appeared naturally in the study of several integrable models in the thermodynamic Bethe ansatz method. The functional generalizations of the identities were conjectured by Gliozzi-Tateo in the mid 90's. They are closely related to another conjecture on the periodicity of the Y-systems by Ravanini-Tateo-Valleriani. These conjectures have been partly proved by several authors with several methods. In this talk we present a proof of the conjectures in full generality based on the cluster algebra/cluster category method recently developed by Fomin-Zelevinsky, Chapoton, Keller and others. The factorization property of the tropical Y-system is the key of the proof. |
