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

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.

81 pages, input files: harvmac, amssym.def, amssym.tex; corrected presentation on odd reflections

References in corpus (25)

• Superconformal Ward Identities and their Solution
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• A three-loop test of the dilatation operator in N=4 SYM
• Index for Orbifold Quiver Gauge Theories
• More on La Grande Bouffe: towards higher spin symmetry breaking in AdS
• Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles
• String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I
• Singularities and closed time-like curves in type IIB 1/2 BPS geometries
• The Spectrum of Yang Mills on a Sphere
• Crystal structures arising from representations of $GL(m|n)$
• Higher spin symmetry (breaking) in N=4 SYM theory and holography
• A Mixed Phase of SUSY Gauge Theories from a-Maximization
• The masses of gauge fields in higher spin field theory on the bulk of $Ad{S}_4$
• Renormalization Group Invariants in the MSSM and Its Extensions
• A wide class of four point functions of BPS operators in N=4 SYM at order g^4
• A Conformally Invariant Holographic Two-Point Function on the Berger Sphere
• AdS_5 Black Holes with Fermionic Hair
• Higher spin holography for SYM in d dimensions
• Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches
• Lifting a Conformal Field Theory from D-Dimensional Flat Space to (D+1)-Dimensional Ads Space
• On twist-two operators in N=4 SYM
• Noncentral extension of the $Ad{S}_5\times S^5$ superalgebra: supermultiplet of brane charges
• SO_0(1,d+1) Racah coefficients: Type I representations
• Superconformal symmetry in the interacting theory of (2,0) tensor multiplets and self-dual strings
• Rationality of the Anomalous Dimensions in N=4 SYM theory

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