N=2 supersymmetric W-algebras

TL;DR

This paper constructs and classifies N=2 super W-algebras extended by an additional super primary field, providing explicit examples up to spin 5/2 and proposing conjectures for their broader classification.

Contribution

It introduces a supersymmetric covariant formalism to explicitly construct N=2 super W-algebras and advances the understanding of their classification.

Findings

Constructed all N=2 super W-algebras up to spin 5/2

Provided explicit examples of algebra extensions

Proposed conjectures on the classification of N=2 SW(1,Δ) algebras

Abstract

We investigate extensions of the N=2 super Virasoro algebra by one additional super primary field and its charge conjugate. Using a supersymmetric covariant formalism we construct all N=2 super W-algebras up to spin 5/2 of the additional generator. Led by these first examples we close with some conjectures on the classification of N=2 ${\cal SW}(1,\Dt)$ algebras.