On thermodynamic approaches to conformal field theory

TL;DR

This paper compares two methods for factorizing the partition function of 2D conformal field theories, revealing their equivalence and introducing a new thermodynamic Bethe ansatz system that offers fresh insights into the model's structure.

Contribution

It demonstrates the equivalence of thermodynamic Bethe ansatz and matrix recursion approaches for 2D CFTs and introduces a novel TBA system with a new dilogarithmic formula for the central charge.

Findings

Both methods are equivalent for SU(2) spinons and 3-state Potts model.

A new TBA system corresponds to a one-quasiparticle representation.

A new dilogarithmic formula for the central charge is derived.

Abstract

We present the thermodynamic Bethe ansatz as a way to factorize the partition function of a 2d field theory, in particular, a conformal field theory and we compare it with another approach to factorization due to K. Schoutens which consists of diagonalizing matrix recursion relations between the partition functions at consecutive levels. We prove that both are equivalent, taking as examples the SU(2) spinons and the 3-state Potts model. In the latter case we see that there are two different thermodynamic Bethe ansatz equation systems with the same physical content, of which the second is new and corresponds to a one-quasiparticle representation, as opposed to the usual two-quasiparticle representation. This new thermodynamic Bethe ansatz system leads to a new dilogarithmic formula for the central charge of that model.