$gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra

TL;DR

This paper introduces a supersymmetric extension of the color Calogero-Sutherland model based on Yangian algebra, demonstrating its integrability through conserved quantities and exploring its algebraic structure and rational limit.

Contribution

It presents a novel supersymmetric model based on Yangian $Y(gl(n|m))$ and analyzes its algebraic structure and integrability properties.

Findings

Conserved quantities generated from super-quantum determinant.

Model exhibits integrability due to commuting conserved quantities.

Rational limit leads to super loop algebra degeneration.

Abstract

A supersymmetric extension of the color Calogero-Sutherland model is considered based on the Yangian $Y(gl(n|m))$. The algebraic structure of the model is discussed in some details. We show that the commuting conserved quantities can be generated from the super-quantum determinant, thus establishing the integrability of the model. In addition, rational limit of the model is studied where the Yangian symmetry degenerates into a super loop algebra.