Reduced qKZ equation and correlation functions of the XXZ model

Details Reduced qKZ equation and correlation functions of the XXZ model Reduced qKZ equation and correlation functions of the XXZ model

2004-12-17

arxiv.org/abs/hep-th/0412191v3

Commun.Math.Phys. 261 (2006) 245-276

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, some formulas revised

Scientific paper

Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (\lambda_1,...,\lambda_{2n}) as (\lambda_1,...,\lambda_n,\lambda_{n}+1,...,\lambda_{1}+1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They can be written as linear combinations of products of two transcendental functions $\tilde{\omega}, \omega$ with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are given by these formulas with an appropriate choice of $\tilde{\omega}, \omega$. We also present a conjectural formula in the massless regime.

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