ADE functional dilogarithm identities and integrable models

TL;DR

This paper introduces a new family of functional equations for the Rogers dilogarithm inspired by integrable quantum field theories, unifying known sum rules and proposing a general conjecture supported by numerical evidence.

Contribution

It presents a novel set of functional identities for the Rogers dilogarithm linked to integrable models, extending classical formulas and conjecturing their universality.

Findings

Derived new functional equations for Rogers dilogarithm

Connected sum rules for central charge to these identities

Supported conjecture with extensive numerical checks

Abstract

We describe a new infinite family of multi-parameter functional equations for the Rogers dilogarithm, generalizing Abel's and Euler's formulas. They are suggested by the Thermodynamic Bethe Ansatz approach to the Renormalization Group flow of 2D integrable, ADE-related quantum field theories. The known sum rules for the central charge of critical fixed points can be obtained as special cases of these. We conjecture that similar functional identities can be constructed for any rational integrable quantum field theory with factorized S-matrix and support it with extensive numerical checks.