New functional dilogarithm identities and sine-Gordon Y-systems

TL;DR

This paper introduces new functional dilogarithm identities linked to sine-Gordon Y-systems and minimal models, revealing a correspondence with rational numbers and exploring their implications for TBA-duality and RG flows.

Contribution

It presents a novel family of multi-parameter functional equations for the Rogers dilogarithm and connects these to sine-Gordon Y-systems and minimal models.

Findings

New functional identities for the Rogers dilogarithm.

A correspondence between rational numbers and these identities.

Discussion on TBA-duality and RG fluxes in minimal models.

Abstract

The sine-Gordon Y-systems and those of the minimal $M_{p,q}+\phi_{13}$ models are determined in a compact form and a correspondence between the rational numbers and a new infinite family of multi-parameter functional equations for the Rogers dilogarithm is pointed out. The relation between the TBA-duality and the massless RG fluxes in the minimal models recently conjectured is briefly discussed.