INTEGRABLE STRUCTURE OF CONFORMAL FIELD-THEORY - II - Q-OPERATOR AND DDV EQUATION

This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators Q(+/-)(lambda) which act in the highest we ight Virasoro module and commute for different values of the parameter lambda. These operators appear to be the CFT analogs of the Q - matri x of Baxter [2], in particular they satisfy Baxter's famous T - Q equa tion. We also show that under natural assumptions about analytic prope rties of the operators Q(lambda) as the functions of lambda the Baxter 's relation allows one to derive the nonlinear integral equations of D estri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We the n use the DDV equation to obtain the asymptotic expansions of the Q-op erators at large lambda; it is remarkable that unlike the expansions o f the T operators of Il], the asymptotic series for Q(lambda) 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 boun dary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point conta ct in the quantum Hall system.