Large N limit of Calogero-Moser models and Conformal Field Theories

TL;DR

This paper explores the large N limit of Calogero-Moser models associated with classical Lie algebras, revealing their connection to two distinct conformal field theories with specific central charges and primary field dimensions.

Contribution

It demonstrates that the large N limit of these models leads to two different conformal field theories, with properties determined by the underlying algebraic symmetries.

Findings

Two distinct conformal field theories emerge in the large N limit.

The central charge c exceeds 1 and is determined by the algebraic symmetry.

Primary field dimensions are dictated by the underlying Lie algebra.

Abstract

We discuss the large N limit of Calogero-Moser models for the classical infinite families of simple Lie algebras A_N, B_N, C_N and D_N. We show that the limit defines two different Conformal Field Theories with central charge c>1. The value of c and the dimension of the primary field are dictated by the underlying algebraic symmetries of the model.