Massless $XXZ$ Model and Degeneration of the Elliptic Algebra $A_{q,p}(\widehat{sl_2})$

Details Massless $XXZ$ Model and Degeneration of the Elliptic Algebra $A_{q,p}(\widehat{sl_2})$ Massless $XXZ$ Model and Degeneration of the Elliptic Algebra $A_{q,p}(\widehat{sl_2})$

1996-10-11

arxiv.org/abs/hep-th/9610079v1

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, PS file, to appear in the proceedings of the conference ``Deformation Theory, Symplectic Geometry and Applications''

Scientific paper

We consider an algebraic structure of the $XXZ$ model in the gapless regime. We argue that a certain degeneration limit of the elliptic algebra $A_{q,p}(\widehat{sl_2})$ 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.

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