R-matrix formulation of affine Yangian of $\hat{\mathfrak{gl}}(1|1)$

TL;DR

This paper develops an R-matrix framework for affine Yangian of 1|1, linking it to 1|1 W-algebras and 1|1 current realization, advancing algebraic understanding in superconformal theories.

Contribution

It introduces an R-matrix for 1|1 superconformal algebras and connects it to the affine Yangian, providing new algebraic tools and insights.

Findings

Defined R-matrix as an intertwiner for 1|1 W-algebras

Established RLL algebra structure for 1|1 affine Yangian

Linked R-matrix approach to current realization of 1|1

Abstract

We study $\mathcal{N}=2$ superconformal field theory and define the R-matrix which acts as an intertwining operator between different realizations of $\mathcal{N}=2$ $W-$algebras of type $A$. Using this R-matrix we define $RLL$ algebra and relate it to current realization of affine Yangian of $\hat{\mathfrak{gl}}(1|1)$.