Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland system

TL;DR

This paper reviews a conformal field theory model for anyons on a circle at finite temperature, establishing a connection to the quantum elliptic Calogero-Sutherland system and providing explicit solutions.

Contribution

It introduces a conformal field theory approach to solve the quantum elliptic Calogero-Sutherland system, including new results on eigenvalues and eigenfunctions.

Findings

Explicit construction of eigenvalues and eigenfunctions for the eCS system

Establishment of a link between anyon models and the eCS system

Extension of the conformal field theory framework to finite temperature

Abstract

We review the construction of a conformal field theory model which describes anyons on a circle and at finite temperature, including previously unpublished results. This anyon model is closely related to the quantum elliptic Calogero-Sutherland (eCS) system. We describe this relation and how it has led to an explicit construction of the eigenvalues and eigenfunctions of the eCS system.