Spectra in Conformal Field Theories from the Rogers Dilogarithm

TL;DR

This paper introduces a universal system of functional relations linked to Bethe ansatz equations and conjectures a new sum formula for the Rogers dilogarithm based on conformal field theory scaling dimensions.

Contribution

It proposes a universal functional relation system and a novel sum formula for the Rogers dilogarithm in the context of conformal field theories.

Findings

New sum formula for Rogers dilogarithm conjectured

Functional relations connected to Bethe ansatz equations established

Insights into scaling dimensions of parafermion conformal field theories

Abstract

We propose a system of functional relations having a universal form connected to the $U_q(X^{(1)}_r)$ Bethe ansatz equation. Based on the analysis of it, we conjecture a new sum formula for the Rogers dilogarithm function in terms of the scaling dimensions of the $X^{(1)}_r$ parafermion conformal field theory.