Two-term dilogarithm identities related to conformal field theory

TL;DR

This paper investigates specific 2x2 matrices related to conformal field theory, deriving new and known dilogarithm identities through analysis of TBA equations and their solutions.

Contribution

It identifies properties of matrices that produce the effective central charge of minimal models and derives new two-term dilogarithm identities.

Findings

Several continuous families and a discrete set of admissible matrices A identified.

New dilogarithm identities obtained and some proven or linked to known identities.

Properties of matrices related to TBA equations in conformal field theory established.

Abstract

We study 2x2 matrices A such that the corresponding TBA equations yield c[A] in the form of the effective central charge of a minimal Virasoro model. Certain properties of such matrices and the corresponding solutions of the TBA equations are established. Several continuous families and a discrete set of admissible matrices A are found. The corresponding two-term dilogarithm identities (some of which appear to be new) are obtained. Most of them are proven or shown to be equivalent to previously known identities.