The master T-operator for the Gaudin model and the KP hierarchy

TL;DR

This paper constructs a master T-operator for the quantum Gaudin model with twisted boundaries, linking it to the KP hierarchy and revealing a connection to the Calogero-Moser system through eigenvalue dynamics.

Contribution

It introduces a novel master T-operator for the Gaudin model that satisfies KP hierarchy equations, establishing a new link between quantum integrable models and classical systems.

Findings

Master T-operator satisfies KP bilinear and Hirota equations.

Eigenvalues of the T-operator correspond to specific KP solutions.

Zeros of the eigenvalues evolve according to the Calogero-Moser dynamics.

Abstract

Following the approach of [arXiv:1112.3310], we construct the master T -operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also characterize the class of solutions to the KP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum Gaudin model and the classical Calogero-Moser system of particles.