Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
This paper is a direct continuation of  where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators Q+/-(λ ) which act in the highest weight Virasoro module and commute for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter , in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV)  for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ it is remarkable that unlike the expansions of the T operators of , the asymptotic series for Q(λ) contains the ``dual'' nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system.
Communications in Mathematical Physics
- Pub Date:
- High Energy Physics - Theory;
- Condensed Matter;
- Mathematics - Quantum Algebra
- Revised version, 43 pages, harvmac.tex. Minor changes, references added