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

Abstract

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

31 pages, 2 figures

References in corpus (5)

• Notes on the K3 Surface and the Mathieu group M_24
• BPS spectrum on AdS${}_3\times$S${}^3\times$S${}^3\times$S${}^1$
• Protected string spectrum in AdS3/CFT2 from worldsheet integrability
• Tensor products of psl(2|2) representations
• An Index for 2D field theories with large N=4 superconformal symmetry