Dilogarithm identities for conformal field theories and cluster algebras: simply laced case

Understand

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.