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October 2, 2025Open Access

Extremal unitary representations of big N=4 superconformal algebra

VKVictor G. KačIIT@MIT PFPierluigi Möseneder FrajriaPolo d’Innovazione di Genomica PPPaolo PapiSapienza University of Rome

Key Points

The classification of extremal unitary representations is confirmed, highlighting massless states within the framework.
The results align with prior conjectures concerning unitary highest weight representations related to minimal W-algebras.
This work completes the proof for the big N=4 superconformal algebra as postulated in earlier studies.
Analysis focuses on the Neveu Schwarz and Ramond sectors, providing a comprehensive understanding of representation theory.

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.

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