Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry

TL;DR

This paper derives explicit character formulae for positive energy unitary irreducible representations of N-extended D=4 conformal superalgebras, advancing the understanding of their structure and classification.

Contribution

It provides the first complete explicit character formulae for N=1 and important cases for N=2 and N=4, building on previous partial results.

Findings

Explicit character formulae for N=1, N=2, and N=4 cases.

Enhanced understanding of the structure of D=4 conformal superalgebra representations.

Foundation for further classification and analysis of superconformal representations.

Abstract

This paper continues the project of constructing the character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). In the first paper we gave the bare characters which represent the defining odd entries of the characters. Now we give the full explicit character formulae for N=1 and for several important examples for N=2 and N=4.