On spectrum of ILW hierarchy in conformal field theory II: coset CFT's

TL;DR

This paper explores the integrable structure of coset conformal field theories, introducing a quantized ILW hierarchy and proposing Bethe ansatz equations to determine its spectrum.

Contribution

It defines a new integrable system related to coset CFTs and formulates Bethe ansatz equations for its spectral analysis.

Findings

Defined a system of Integrals of Motion depending on external parameters.

Proposed Bethe ansatz equations for the spectrum of the quantized ILW hierarchy.

Connected the integrable structure to coset conformal field theories.

Abstract

We study integrable structure of the coset conformal field theory and define the system of Integrals of Motion which depends on external parameters. This system can be viewed as a quantization of the ILW type hierarchy. We propose a set of Bethe anzatz equations for its spectrum.