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29 March 2024
 
  » arxiv » hep-th/9412229

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Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
V. Bazhanov ; S. Lukyanov ; A. Zamolodchikov ;
Date 29 Dec 1994
Journal Commun.Math.Phys. 177 (1996) 381-398
Subject hep-th
AbstractWe construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${f T}$-operators’’, act in highest weight Virasoro modules. The ${f T}$-operators depend on the spectral parameter $lambda$ and their expansion around $lambda = infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${f T}$-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}over {2n+3}} , n=1,2,3,... $of the Virasoro central charge the eigenvalues of the ${f T}$-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 ${cal M}_{2,2n+3}$; 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 $Phi_{1,3}$. The relation of these ${f T}$-operators to the boundary states is also briefly described.
Source arXiv, hep-th/9412229
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