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

Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi

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 [11]. 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 [15], [17], and complete their proof for the $big\ N=4$ superconformal algebra.