Integrable Boundaries and Universal TBA Functional Equations

TL;DR

This paper derives universal TBA functional equations for critical lattice models related to conformal field theories, emphasizing their independence from specific boundary conditions and their reliance on Coxeter numbers.

Contribution

It introduces a universal derivation of TBA functional equations for A-D-E lattice models, applicable to various boundary conditions and related to rational CFTs.

Findings

Derived fusion hierarchy of functional equations for A-D-E models.

Established universality of TBA equations depending only on Coxeter number.

Conjectured universality of TBA equations for all rational CFT lattice models.

Abstract

We derive the fusion hierarchy of functional equations for critical A-D-E lattice models related to, the sl(2) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory, and deduce the related TBA functional equations. The derivation uses fusion projectors and applies in the presence of all known integrable boundary conditions on the torus and cylinder. The resulting TBA functional equations are_universal_ in the sense that they depend only on the Coxeter number of the A-D-E graph and are independent of the particular integrable boundary conditions. We conjecture generally that TBA functional equations are universal for all integrable lattice models associated with rational CFTs and their integrable perturbations.