Random Matrix Model and the Calogero-Sutherland Model: A Novel Current-Density Mapping

TL;DR

This paper establishes a new local current-density mapping in the Calogero-Sutherland model that relates correlators for any coupling strength, including irrational values, extending the understanding of invariant correlators in random matrix theory and integrable systems.

Contribution

It introduces a novel local current-density mapping for arbitrary coupling in the Calogero-Sutherland model, expanding the connection between random matrix theory and integrable systems.

Findings

Derived a current-density relationship valid for all coupling values.

Extended the mapping to irrational coupling strengths.

Identified additional current-density correlations beyond Ward identities.

Abstract

We investigate the relation between the invariant correlators of random matrix theory and correlators of the integrable one-dimensional systems. Starting from the relation between correlators for the coupling strengths $\lambda =1/ 2$, $1$, and $2$, we explore the local current-density mapping applicable to arbitrary $\lambda$ including {\em irrational\/} values, which results from the novel structure of the Calogero-Sutherland model. We find an interesting and novel relationship between equal time current and density correlations for any coupling, which exist {\em in addition} to the usual Ward Identities for this class of systems.