# Conformal field theory, solitons, and elliptic Calogero--Sutherland models

## TL;DR

This paper constructs a conformal field theory on a torus that enables second quantization of the elliptic Calogero-Sutherland model and relates it to a quantum soliton equation, revealing new links between CFT, solitons, and integrable models.

## Contribution

It introduces a non-chiral CFT framework that simultaneously quantizes the elliptic Calogero-Sutherland model and a quantum soliton equation, expanding the understanding of their interrelation.

## Key findings

- Developed a non-chiral CFT on the torus for eCS model quantization.
- Linked the CFT operator to a quantum soliton equation (ncILW).
- Proposed a particle interpretation of solitons in the quantum ncILW context.

## Abstract

We construct a non-chiral conformal field theory (CFT) on the torus that accommodates a second quantization of the elliptic Calogero-Sutherland (eCS) model. We show that the CFT operator that provides this second quantization defines, at the same time, a quantum version of a soliton equation called the non-chiral intermediate long-wave (ncILW) equation. We also show that this CFT operator is a second quantization of a generalized eCS model which can describe arbitrary numbers of four different kinds of particles; we propose that these particles can be identified with solitons of the quantum ncILW equation.