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

## TL;DR

This paper proves dilogarithm identities related to conformal field theories and cluster algebras for simply laced Dynkin diagrams, confirming longstanding conjectures using cluster algebra techniques.

## Contribution

It provides a complete proof of dilogarithm identities for simply laced types, extending previous partial results and conjectures.

## Key findings

- Proved dilogarithm identities for all simply laced Dynkin diagrams.
- Confirmed conjectures by Bazhanov, Kirillov, Reshetikhin, Gliozzi, and Tateo.
- Established a cluster algebra framework for Y-systems in this context.

## Abstract

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.