TY - JOUR

T1 - Minimal unitary representation of 5d superconformal algebra F(4) and AdS6/CFT5 higher spin (super)-algebras

AU - Fernando, Sudarshan

AU - Günaydin, Murat

N1 - Funding Information:
One of us (M.G.) would like to thank the CERN Theory Division and the Albert Einstein Institute for their hospitality where part of this work was done. The research of M.G. is supported in part by the U.S. Department of Energy under DOE Grant No: DE-SC0010534 . S.F. would like to thank the Center for Fundamental Theory of the Institute for Gravitation and the Cosmos at Pennsylvania State University, where part of this work was done. We would like to thank Karan Govil, Evgeny Skvortsov and Massimo Taronna for stimulating discussions regarding higher spin algebras.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar field in five dimensions and admits a unique "deformation" which describes a massless conformal spinor. Scalar and spinor minreps of SO(5,2) are the 5. d analogs of Dirac's singletons of SO(3,2). We then construct the minimal unitary representation of the unique 5. d superconformal algebra F(4) with the even subalgebra SO(5,2)×SU(2). The minrep of F(4) describes a massless conformal supermultiplet consisting of two scalar and one spinor fields. We then extend our results to the construction of higher spin AdS6/CFT5 (super)-algebras. The Joseph ideal of the minrep of SO(5,2) vanishes identically as operators and hence its enveloping algebra yields the AdS6/CFT5 bosonic higher spin algebra directly. The enveloping algebra of the spinor minrep defines a "deformed" higher spin algebra for which a deformed Joseph ideal vanishes identically as operators. These results are then extended to the construction of the unique higher spin AdS6/CFT5 superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.

AB - We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar field in five dimensions and admits a unique "deformation" which describes a massless conformal spinor. Scalar and spinor minreps of SO(5,2) are the 5. d analogs of Dirac's singletons of SO(3,2). We then construct the minimal unitary representation of the unique 5. d superconformal algebra F(4) with the even subalgebra SO(5,2)×SU(2). The minrep of F(4) describes a massless conformal supermultiplet consisting of two scalar and one spinor fields. We then extend our results to the construction of higher spin AdS6/CFT5 (super)-algebras. The Joseph ideal of the minrep of SO(5,2) vanishes identically as operators and hence its enveloping algebra yields the AdS6/CFT5 bosonic higher spin algebra directly. The enveloping algebra of the spinor minrep defines a "deformed" higher spin algebra for which a deformed Joseph ideal vanishes identically as operators. These results are then extended to the construction of the unique higher spin AdS6/CFT5 superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.

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U2 - 10.1016/j.nuclphysb.2014.11.015

DO - 10.1016/j.nuclphysb.2014.11.015

M3 - Article

AN - SCOPUS:84916899042

VL - 890

SP - 570

EP - 605

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -