Massless $XXZ$ Model and Degeneration of the Elliptic Algebra $A_{q,p}(\widehat{s{l}_2})$

Abstract

We consider an algebraic structure of the $XXZ$ model in the gapless regime. We argue that a certain degeneration limit of the elliptic algebra $A_{q,p}(\widehat{s{l}_2})$ is a relevant object. We give a free boson realization of this limiting algebra and derive an integral formula for the correlation function. The result agrees with the one obtained by solving a system of difference equations. We also discuss the relation of our algebra to the deformed Virasoro algebra and Lukyanov's bosonization of the sine-Gordon theory.

22 pages, PS file, to appear in the proceedings of the conference ``Deformation Theory, Symplectic Geometry and Applications'', Centro Stefano Franscini of ETH Zürich, Monte Verità, CH-6612 Ascona, June 16-22, 1996