Extremal unitary representations of big $N=4$ superconformal algebra

TL;DR

This paper provides a detailed proof classifying extremal (massless) unitary highest weight representations of the big N=4 superconformal algebra, confirming conjectures and completing their proof for this algebra.

Contribution

It offers a comprehensive proof of the classification of extremal unitary representations of the big N=4 superconformal algebra, extending previous conjectures.

Findings

Confirmed the classification of extremal unitary representations.

Aligned results with existing conjectures on minimal W-algebras.

Completed the proof for the big N=4 superconformal algebra.

Abstract

In this paper we give a detailed proof of the classification of extremal (=massless) unitary highest weight representations in the Neveu Schwarz and Ramond sectors of the big $N=4$ superconformal algebra which can be found in [5]. Our results agree with the general conjectures about classification of unitary highest weight representation of minimal $W$-algebras attached to basic Lie superalgebras formulated in [10], [11], and complete their proof for the big $N=4$ superconformal algebra.