Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations
Kazunori Kuroki, Atsushi Nakayashiki
TL;DR
This paper derives integral solutions to the quantum Knizhnik-Zamolodchikov equations using free field realizations, confirming their equivalence with existing formulas by Tarasov and Varchenko.
Contribution
It introduces a free field approach to solve qKZ equations for $U_q(\hat{sl}_2)$ and demonstrates the equivalence with known integral formulas.
Findings
Integral formulas from free field realization match Tarasov and Varchenko's results.
Provides a new perspective on solutions of qKZ equations via free field methods.
Confirms the consistency of different solution approaches for quantum affine algebras.
Abstract
Solutions of the qKZ equation associated with the quantum affine algebra and its two dimensional evaluation representation are studied. The integral formulae derived from the free field realization of intertwining operators of -Wakimoto modules are shown to coincide with those of Tarasov and Varchenko.
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