Integrable Structure of Conformal Field Theory II. Qoperator and DDV equation
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 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 [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 Destride Vega (DDV) [3] for the eigenvalues of the Qoperators. 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 sineGordon 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1997
 DOI:
 10.1007/s002200050240
 arXiv:
 arXiv:hepth/9604044
 Bibcode:
 1997CMaPh.190..247B
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter;
 Mathematics  Quantum Algebra
 EPrint:
 Revised version, 43 pages, harvmac.tex. Minor changes, references added