A construction of N=2 and centerless N=4 superconformal fields via affine superalgebras

TL;DR

This paper introduces a novel method to construct N=2 and centerless N=4 superconformal algebras using affine superalgebras and free bosonic fields, enhancing understanding of their algebraic structures.

Contribution

It provides new explicit constructions of N=2 and N=4 superconformal algebras from affine superalgebras and free bosonic fields, with added insights on commutants and invariant subspaces.

Findings

Constructed N=2 superconformal algebra from ${sl}(2|1)$ currents

Constructed N=4 superconformal algebra without central charge from ${sl}(2|2)$ currents

Analyzed commutants and invariant subspaces within these algebraic frameworks

Abstract

In this note we give a new construction of the N=2 superconformal algebra using currents of the affine superalgebra $\hat{sl}(2 | 1)$ and free bosonic fields, and also the N=4 superconformal algebra without central charge in terms of currents of $\hat{sl}(2 | 2)$ and free bosonic fields. Arguments on commutants and invariant subspaces are added.