New N=1 Extended Superconformal Algebras with Two and Three Generators

TL;DR

This paper classifies and constructs extended superconformal algebras with one, two, and three generators, expanding the super Virasoro algebra and revealing new algebraic structures and subalgebras.

Contribution

It provides a systematic classification of SW-algebras with up to three generators and introduces new algebraic structures, including subalgebras and realizations.

Findings

Classified SW-algebras with one generator up to dimension 7.

Identified SW(3/2, 11/2) as a subalgebra of SW(3/2, 5/2) at c=10/7.

Constructed new SW-algebras with three generators.

Abstract

In this paper we consider extensions of the super Virasoro algebra by one and two super primary fields. Using a non-explicitly covariant approach we compute all SW-algebras with one generator of dimension up to 7 in addition to the super Virasoro field. In complete analogy to W-algebras with two generators most results can be classified using the representation theory of the super Virasoro algebra. Furthermore, we find that the SW(3/2, 11/2)-algebra can be realized as a subalgebra of SW(3/2, 5/2) at c = 10/7. We also construct some new SW-algebras with three generators, namely SW(3/2, 3/2, 5/2), SW(3/2, 2, 2) and SW(3/2, 2, 5/2).