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:
Report number:
  • CLNS-94-1316,
  • RU-94-98

Citations per year

19952003201120192025051015202530
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{\bf T}-operators'', act in highest weight Virasoro modules. The T{\bf T}-operators depend on the spectral parameter λ\lambda and their expansion around λ=\lambda = \infty generates an infinite set of commuting Hamiltonians of the quantum KdV system. The T{\bf 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=13(2n+1) 22n+3,n=1,2,3,...c=1-3{{(2n+1)~2}\over {2n+3}} , n=1,2,3,... of the Virasoro central charge the eigenvalues of the T{\bf 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 M2,2n+3{\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 Φ1,3\Phi_{1,3}. The relation of these T{\bf T}-operators to the boundary states is also briefly described.
  • field theory: conformal
  • dimension: 2
  • Korteweg-de Vries equation
  • integrability
  • Bethe ansatz
  • S-matrix