TBA equations for integrable perturbed SU(2)_k × SU(2)_l SU(2)_k+1 coset models

Two sets of thermodynamic Bethe ansatz systems of massive and massless nature respectively are conjectured. They seem relevant to describe the finite-size ground-state energy in SU(2)_k × SU(2)_l SU(2)_k+1 coset models perturbed by the relevant integrable operator [(k, 0) ⊗ (l,0)/(k+l, 1)] (in terms of the GKO branchings) with negative and positive couplings. Different limits l → ∞ or k,l → ∞ lead to infinite TBA systems describing either the asymptotically free JJ perturbations of the WZW models SU(2)_k or the asymptotically free SU(2) × SU(2) principal chiral model with Wess-Zumino term. Although we have no general derivation of these systems on the grounds of factorized scattering theory, they predict the expected behavior both at small and large distances. We believe that these systems describe exactly the Casimir energy in the perturbed SU(2) cosets.