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
We obtain exactly the vacuum expectation values (∂ϕ) 2 (∂ϕ) e iαϕ in the sine-Gordon model and L −2L−2 Φ l,k in Φ 1,3 perturbed minimal CFT. We discuss applications of these results to short-distance expansions of two-point correlation functions.May, 98
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
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