Affine Yangian of $\mathfrak{gl}(2)$ and integrable structures of superconformal field theory

TL;DR

This paper explores the connection between the affine Yangian of gl(2) and integrable structures in superconformal field theory, deriving relations and Bethe ansatz equations for spectral analysis.

Contribution

It establishes the relation between RLL and current realizations of the affine Yangian of gl(2) and proves Bethe ansatz equations for the spectrum of integrals of motion.

Findings

Derived relation between RLL and current realizations.

Proved Bethe ansatz equations for integrals of motion.

Linked affine Yangian structures to superconformal field theory.

Abstract

This paper is devoted to study of integrable structures in superconformal field theory and more general coset CFT's related to the affine Yangian $\textrm{Y}\big(\widehat{\mathfrak{gl}}(2)\big)$. We derive the relation between the RLL and current realizations and prove Bethe anzatz equations for the spectrum of Integrals of Motion.