Abstract:
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 ${\bf Q}_{\pm}(\lambda)$ 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 [2], 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) [3] 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 [1], 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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 2 December 1996 / Accepted: 11 March 1997
Rights and permissions
About this article
Cite this article
Bazhanov, V., Lukyanov, S. & Zamolodchikov, A. Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation . Comm Math Phys 190, 247–278 (1997). https://doi.org/10.1007/s002200050240
Issue Date:
DOI: https://doi.org/10.1007/s002200050240