Opers for higher states of the quantum Boussinesq model

TL;DR

This paper explores the connection between differential operators and the quantum Boussinesq model, demonstrating how monodromy data solve Bethe Ansatz equations for all states of the system.

Contribution

It establishes a comprehensive ODE/IM correspondence for all states of the quantum Boussinesq model using third order differential operators.

Findings

Monodromy data solve Bethe Ansatz equations.

The correspondence applies to all states of the model.

Provides a new analytical approach to quantum integrable systems.

Abstract

We study the ODE/IM correspondence for all the states of the quantum Boussinesq model. We consider a particular class of third order linear ordinary differential operators and show that the generalised monodromy data of such operators provide solutions to the Bethe Ansatz equations of the Quantum Boussinesq model.