We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as "T-operators", act in highest weight Virasoro modules. The T-operators depend on the spectral parameter λ and their expansion around λ = ∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The T-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices 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-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory M 2,2n+3 ; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ 1,3 . The relation of these T-operators to the boundary states is also briefly described.

This paper is a direct continuation of [1] where we begun the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators

In this paper we fill some gaps in the arguments of our previous papers [1,2]. In particular, we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining relations of the Yang-Baxter algebra. Among other results we present a derivation of the functional relations satisfied by T and Q operators and a proof of the basic analyticity assumptions for these operators used in [1,2]. J 12 J 13 J 14 J 23 J 24 J 34

The eigenvalues of the transfer matrix of the generalized RSOS model are exactly calculated. From the consideration of the thermodynamics of the quantum system on the one-dimensional chain connected with the RSOS model, we calculate the central charges of the effective conformal field theories describing the critical behavior of the model in different regimes.

In this paper we study the Yang-Baxter integrable structure of Conformal Field Theories with extended conformal symmetry generated by the W 3 algebra. We explicitly construct various T and Q-operators which act in the irreducible highest weight modules of the W 3 algebra. These operators can be viewed as continuous field theory analogues of the commuting transfer matrices and Q-matrices of the integrable lattice systems associated with the quantum algebra U q ( sl (3)). We formulate several conjectures detailing certain analytic characteristics of the Q-operators and propose exact asymptotic expansions of the T and Q-operators at large values of the spectral parameter. We show, in particular, that the asymptotic expansion of the T-operators generates an infinite set of local integrals of motion of the W 3 CFT which in the classical limit reproduces an infinite set of conserved Hamiltonians associated with the classical Boussinesq equation. We further study the vacuum eigenvalues of the Q-operators (corresponding to the highest weight vector of the W 3 module) and show that they are simply related to the expectation values of the boundary exponential fields in the non-equilibrium boundary affine Toda field theory with zero bulk mass.

No abstract

It has recently been shown that the solvable N-state chiral Potts model is related to a vertex model with N-state spins on vertical edges, two-state spins on horizontal edges. Here we generalize this to a “j-state by N-state” model and establish three sets of functional relations between the various transfer matrices. The significance of the “super-integrable” case of the chiral Potts model is discussed, and results reported for its finite-size corrections at criticality.

We develop a method of computing the excited state energies in Integrable Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate compactified on a circle of circumference R. The IQFT "commuting transfer-matrices" introduced in [1] for Conformal Field Theories (CFT) are generalized to non-conformal IQFT obtained by perturbing CFT with the operator Φ 1,3 . We study the models in which the fusion relations for these "transfer-matrices" truncate and provide closed integral equations which generalize the equations of Thermodynamic Bethe Ansatz to excited states. The explicit calculations are done for the first excited state in the "Scaling Lee-Yang Model".We have also shown that the "fusion relations" for the operators T j (λ)1 These operators appear as the continuous QFT versions of Baxter's commuting transfermatrices [7], [8] and therefore we maintain using this term although the original meaning of the term "transfer-matrix" here is apparently lost.