Multidimensional Calogero systems from matrix models

TL;DR

This paper demonstrates how a specific matrix model leads to multidimensional Calogero-Sutherland systems and their spin variants, revealing connections to Yang-Mills dimensional reduction and D0-brane dynamics.

Contribution

It introduces a matrix model framework that produces multidimensional Calogero systems and links them to Yang-Mills theories and D-brane physics.

Findings

Matrix model yields multidimensional Calogero-Sutherland models.

Solutions to the matrix equations demonstrate model properties.

Connection established between matrix models and D0-brane dynamics.

Abstract

We show that a particular many-matrix model gives rise, upon hamiltonian reduction, to a multidimensional version of the Calogero-Sutherland model and its spin generalizations. Some simple solutions of these models are demonstrated by solving the corresponding matrix equations. A connection of this model to the dimensional reduction of Yang-Mills theories to (0+1)-dimensions is pointed out. In particular, it is shown that the low-energy dynamics of D0-branes in sectors with nontrivial fermion content is that of spin-Calogero particles.