Solutions of coupled BPS equations for two-family Calogero and matrix models

TL;DR

This paper analyzes coupled BPS equations in two-family Calogero and matrix models, providing a full classification of static soliton solutions in the large N limit using collective-field methods.

Contribution

It offers the first complete classification of solutions to coupled BPS equations in these models, including exact solutions in the strong-weak dual case.

Findings

All solutions close to constant are identified.

Exact one-parameter solutions are constructed in the dual case.

A comprehensive classification of static soliton solutions is achieved.

Abstract

We consider a large N, two-family Calogero and matrix model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the solutions to the coupled Bogomol'nyi-Prasad-Sommerfeld equations are given by the static soliton configurations. We find all solutions close to constant and construct exact one-parameter solutions in the strong-weak dual case. Full classification of these solutions is presented.