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

TL;DR

This paper classifies unitary representations of the large  superconformal algebra using Young supertableaux and analyzes their contribution to a supersymmetric index, advancing understanding of superalgebra representations.

Contribution

It introduces a classification method for  superconformal algebra representations via Young supertableaux and explores their role in supersymmetric indices.

Findings

Classified  superconformal algebra representations using Young supertableaux.

Analyzed the contribution of these representations to the supersymmetric index.

Provided a framework for understanding states in the Ramond sector.

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.