On relation of the genus one Moore-Seiberg identity to the Baxter Q-operator in the hyperbolic Ruijsenaars model

TL;DR

This paper connects the Moore-Seiberg duality identity in Liouville conformal field theory to the Baxter Q-operator and eigenfunction formulas in the hyperbolic Ruijsenaars model, revealing a deep link between CFT and integrable systems.

Contribution

It demonstrates how the genus one Moore-Seiberg identity underpins key operators and eigenfunctions in the hyperbolic Ruijsenaars integrable system, a novel theoretical insight.

Findings

Derived the Baxter Q-operator from Moore-Seiberg identity

Connected eigenfunction product formulas to CFT duality

Suggested a fundamental role of Moore-Seiberg in integrability

Abstract

In this paper we show how the Baxter Q-operator and the product formula for eigenfunctions of two-particle hyperbolic Ruijsenaars system can be derived from the genus one Moore-Seiberg duality identity in two-dimensional Liouville conformal field theory. We expect that this relation would reveal genuine role of the Moore-Seiberg identity in integrable systems.