Young supertableaux and the large ${ \mathcal N }=4$ superconformal algebra

Abstract

In this paper we consider unitary highest weight irreducible representations\nof the `Large' $\\mathcal{N}=4$ superconformal algebra $A_\\gamma$ in the Ramond\nsector as infinite-dimensional graded modules of its zero mode subalgebra,\n$\\mathfrak{su}(2|2)$. We describe how representations of $\\mathfrak{su}(2|2)$\nmay be classified using Young supertableaux, and use the decomposition of\n$A_\\gamma$ as an $\\mathfrak{su}(2|2)$ module to discuss the states which\ncontribute to the supersymmetric index $I_1$, previously proposed in the\nliterature by Gukov, Martinec, Moore and Strominger.\n