Two-Term Dilogarithm Identities Related to Conformal Field Theory

We study 2 × 2 matrices A such that the corresponding thermodynamic Bethe ansatz (TBA) equations yield 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.