Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions

Journal Article · Sun Aug 15 04:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3447773· OSTI ID:21476529

Fernando, Sudarshan; Guenaydin, Murat ^[1]

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1. Department of Physical Sciences, Kutztown University, Kutztown, Pennsylvania 19530 (United States)

We study the minimal unitary representation (minrep) of SO(4,2) over a Hilbert space of functions of three variables, obtained by quantizing its quasiconformal action on a five dimensional space. The minrep of SO(4,2), which coincides with the minrep of SU(2,2) similarly constructed, corresponds to a massless conformal scalar in four space-time dimensions. There exists a one-parameter family of deformations of the minrep of SU(2,2). For positive (negative) integer values of the deformation parameter {zeta}, one obtains positive energy unitary irreducible representations corresponding to massless conformal fields transforming in (0,{zeta}/2)((-{zeta}/2,0)) representation of the SL(2,C) subgroup. We construct the supersymmetric extensions of the minrep of SU(2,2) and its deformations to those of SU(2,2|N). The minimal unitary supermultiplet of SU(2,2|4), in the undeformed case, simply corresponds to the massless N=4 Yang-Mills supermultiplet in four dimensions. For each given nonzero integer value of {zeta}, one obtains a unique supermultiplet of massless conformal fields of higher spin. For SU(2,2|4), these supermultiplets are simply the doubleton supermultiplets studied in the work of Gunaydin et al. [Nucl. Phys. B 534, 96 (1998); e-print arXiv:hep-th/9806042].

• OSTI ID: 21476529
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BANACH SPACE
CONFORMAL INVARIANCE
ELEMENTARY PARTICLES
FIELD THEORIES
HILBERT SPACE
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
MASSLESS PARTICLES
MATHEMATICAL SPACE
MULTIPLETS
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
SCALARS
SO GROUPS
SO-4 GROUPS
SPACE
SPACE-TIME
SPIN
SU GROUPS
SU-2 GROUPS
SUPERMULTIPLETS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
UNITARY SYMMETRY
YANG-MILLS THEORY