Integrable Boundaries and Universal TBA Functional Equations

C. H. Otto Chui , Christian Mercat (1) , Paul A. Pearce

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: statistical mechanics; integrable models; boundary conditions; conformal field theory; thermodynamic Bethe Ansatz

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique des Hautes Energies - Réseau [hep-lat]; Algèbres d'opérateurs [math.OA]

C. H. Otto Chui, Christian Mercat, Paul A. Pearce. Integrable Boundaries and Universal TBA Functional Equations. Kashiwara M.; Miwa T. MathPhys Odyssey 2001, 23, Birkhäuser, pp.391-413, 2002, Progress in Mathematical Physics, 978-1-4612-6605-1. ⟨10.1007/978-1-4612-0087-1_14⟩. ⟨hal-00248892⟩