Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
Dec, 1994
24 pages
Published in:
- Commun.Math.Phys. 177 (1996) 381-398
e-Print:
- hep-th/9412229 [hep-th]
DOI:
Report number:
- CLNS-94-1316,
- RU-94-98
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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 ``-operators'', act in highest weight Virasoro modules. The -operators depend on the spectral parameter and their expansion around generates an infinite set of commuting Hamiltonians of the quantum KdV system. The -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 of the Virasoro central charge the eigenvalues of the -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 ; 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 . The relation of these -operators to the boundary states is also briefly described.- field theory: conformal
- dimension: 2
- Korteweg-de Vries equation
- integrability
- Bethe ansatz
- S-matrix
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