Conformal field theory and integrable systems associated with elliptic curves

TL;DR

This paper introduces an elliptic quantum group derived from quantizing the Knizhnik-Zamolodchikov-Bernard equation on a torus, establishing connections with elliptic IRF models and integrable systems.

Contribution

It proposes a new elliptic quantum group framework based on the quantization of the KZB equation, linking conformal field theory and integrable models.

Findings

Elliptic quantum groups are constructed from the KZB equation.

The relation between elliptic quantum groups and IRF models is clarified.

The approach bridges conformal field theory and integrable systems on elliptic curves.

Abstract

An elliptic version of quantum groups is proposed. It comes form the quantization of the Knizhnik-Zamolodchikov- Bernard equation on the torus. The relation with elliptic IRF models is explained.