Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry

TL;DR

This paper derives character formulas for positive energy unitary irreducible representations of N-extended D=4 conformal superalgebras, providing insights into their structure and decompositions at the unitarity threshold.

Contribution

It introduces explicit character formulas for these superalgebras and analyzes the decomposition of long superfields at the unitarity threshold, extending previous representation theory results.

Findings

Character formulas for positive energy UIRs of su(2,2/N)

Decomposition of long superfields at unitarity threshold

Applicability to irreps of sl(4/N) superalgebras

Abstract

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of su(2,2/N) developed already in the 80s.