Yangian associated with 2D $\mathcal{N}=1$ SCFT

TL;DR

This paper explores the Yangian symmetry linked to 2D $ =1$ superconformal field theory, connecting integrable models, algebraic structures, and supersymmetric extensions of known models.

Contribution

It introduces a Yangian associated with $ =1$ superconformal algebra, extending the Calogero-Sutherland model to include supersymmetry.

Findings

Relation between Yangian and $ =1$ superconformal algebra clarified

Supersymmetric Calogero-Sutherland model analyzed

Connections with $ ext{W}_n$ algebra and integrable models established

Abstract

Recently, Maulik and Okounkov proposed an integrable lattice model where the degree of freedom at each site is identical to the Hilbert space of free boson in two dimensions. We give a brief review of their construction and explain the relation with $\mathcal{W}_n$ algebra and Calogero-Sutherland model. As a generalization, we examine the Yangian associated with $\mathcal{N}=1$ superconformal algebra which describes a supersymmetric extension of Calogero-Sutherland model and compare it with the literature.