TY - JOUR

T1 - Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions

AU - Fernando, Sudarshan

AU - Günaydin, Murat

N1 - Funding Information:
This work was supported in part by the National Science Foundation under Grant Nos. PHY-0555605 and PHY-0855356. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

PY - 2010/8

Y1 - 2010/8

N2 - 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 ζ, one obtains positive energy unitary irreducible representations corresponding to massless conformal fields transforming in (0,ζ/2)((-ζ/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{pipe}N). The minimal unitary supermultiplet of SU(2,2{pipe}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 ζ, one obtains a unique supermultiplet of massless conformal fields of higher spin. For SU(2,2{pipe}4), these supermultiplets are simply the doubleton supermultiplets studied in the work of Gunaydin et al. [Nucl. Phys. B534, 96 (1998); e-print arXiv:hep-th/9806042].

AB - 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 ζ, one obtains positive energy unitary irreducible representations corresponding to massless conformal fields transforming in (0,ζ/2)((-ζ/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{pipe}N). The minimal unitary supermultiplet of SU(2,2{pipe}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 ζ, one obtains a unique supermultiplet of massless conformal fields of higher spin. For SU(2,2{pipe}4), these supermultiplets are simply the doubleton supermultiplets studied in the work of Gunaydin et al. [Nucl. Phys. B534, 96 (1998); e-print arXiv:hep-th/9806042].

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U2 - 10.1063/1.3447773

DO - 10.1063/1.3447773

M3 - Article

AN - SCOPUS:78049417534

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 8

M1 - 082301

ER -