INTEGRABLE STRUCTURE OF CONFORMAL FIELD-THEORY, QUANTUM KDV THEORY AND THERMODYNAMIC BETHE-ANSATZ

We construct the quantum versions of the monodromy matrices of KdV the ory. The traces of these quantum monodromy matrices, which will be cal led as ''T-operators,'' act in highest weight Virasoro modules. The T- operators depend on the spectral parameter lambda and their expansion around lambda = infinity generates an infinite set of commuting Hamilt onians of the quantum KdV system. The T-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values c = 1 - 3(2n+1)2/2n+3 n = 1,2,3... of the Virasoro central charge the eigenvalues of the T-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-stat e eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field t heory M(2,2n+3); in general they provide a way to generalize the techn ique of the Thermodynamic Bethe Ansatz to the excited states. We discu ss a generalization of our approach to the cases of massive field theo ries obtained by perturbing these Conformal Field Theories with the op erator phi(1,3). The relation of these T-operators to the boundary sta tes is also briefly described.