Lift of dilogarithm to partition identities

TL;DR

This paper establishes a connection between dilogarithm identities and partition identities derived from characters of conformal field theories related to certain scattering theories, proposing a possible generalization of this correspondence.

Contribution

It introduces a method to lift dilogarithm identities to partition identities involving conformal field theory characters, expanding understanding of their mathematical structure.

Findings

Partition identities derived from conformal characters.

Dilogarithm identities obtained via modular invariance.

Proposal of a generalization from dilogarithm to partition identities.

Abstract

For the whole set of dilogarithm identities found recently using the thermodynamic Bethe-Ansatz for the $ADET$ series of purely elastic scattering theories we give partition identities which involve characters of those conformal field theories which correspond to the UV-limits of the scattering theories. These partition identities in turn allow to derive the dilogarithm identities using modular invariance and a saddle point approximation. We conjecture on possible generalizations of this correspondance, namely, a lift from dilogarithm to partition identities.