Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz

Vladimir V. Bazhanov, Sergei L. Lukyanov, Alexander B. Zamolodchikov

Research output: Contribution to journalArticlepeer-review

324 Scopus citations


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 transfermatrices 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 the massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ℳ2, 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 these T-operators to the boundary states is also briefly described.

Original languageEnglish (US)
Pages (from-to)381-398
Number of pages18
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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