Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz |
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Authors: | Vladimir V Bazhanov Sergei L Lukyanov Alexander B Zamolodchikov |
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Institution: | 1. Department of Theoretical Physics and Center of Mathematics and its Applications, IAS Australian National University, 0200, Canberra, ACT, Australia 3. Newman Laboratory, Cornell University, 14853-5001, Ithaca, NY, USA 4. Department of Physics and Astronomy, Rutgers University, 08855-049, Piscataway, NJ, USA 5. L.D. Landau Institute for Theoretical Physics, 142432, Chernogolovka, Russia
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Abstract: | 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. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-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 $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-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 the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM 2,2n+3; in general they provide a way to generalize the technique of the 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 Φ1,3. The relation of theseT-operators to the boundary states is also briefly described. |
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