Quantum Knizhnik--Zamolodchikov equation for $U_q (\widehat{ sl_n})$ and integral formula

TL;DR

This paper derives an integral formula for solutions to the quantum Knizhnik--Zamolodchikov equation associated with the quantum affine algebra $U_q( ext{sl}_n)$, generalizing previous results for $U_q( ext{sl}_2)$ and form factors in $SU(n)$ models.

Contribution

It provides a new integral formula for the quantum KZ equation solutions for $U_q( ext{sl}_n)$, extending earlier work on $U_q( ext{sl}_2)$ and form factors in integrable models.

Findings

Generalized integral formula for $U_q( ext{sl}_n)$ KZ solutions

Unified framework extending previous $U_q( ext{sl}_2)$ results

Connections to form factors in $SU(n)$ chiral Gross-Neveu model

Abstract

Presented is an integral formula for solutions to the quantum Knizhnik--Zamolodchikov equation of level $0$ associated with the vector representation of $U_q (\widehat{ sl_n})$. This formula gives a generalization of both our previous work for $U_q (\widehat{ sl_2})$ and Smirnov's formula for form factors of $SU(n)$ chiral Gross-Neveu model.