From Vertex Operators to Calogero-Sutherland Models

TL;DR

This paper connects vertex operator correlation functions with generalized Calogero-Sutherland models through Ward identities and W_infinity algebra, revealing new insights into their mathematical structure and ground state wave functions.

Contribution

It introduces a novel link between vertex operator algebra and generalized Calogero-Sutherland Hamiltonians, extending the understanding of their mathematical and physical relations.

Findings

Correlation functions satisfy Ward identities related to W_infinity algebra.

Ground state wave function expressed via vertex operators.

Generalization of Calogero-Sutherland Hamiltonians derived from vertex algebra.

Abstract

The correlation function of the product of N generalized vertex operators satisfies an infinite set of Ward identities, related to a W_{\infty} algebra, whose extention out of the mass shell gives rise to equations which can be considered as a generalization of the compactified Calogero-Sutherland (CS) hamiltonians. In particular the wave function of the ground state of the compactified CS model is shown to be given by the value of the product of N vertex operators between the vacuum and exitated state. The role of vertex algebra as underlying unifying structure is pointed out.