### Abstract

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 AdS_{6}/CFT_{5} (super)-algebras. The Joseph ideal of the minrep of SO(5,2) vanishes identically as operators and hence its enveloping algebra yields the AdS_{6}/CFT_{5} 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 AdS_{6}/CFT_{5} superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.

Original language | English (US) |
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Pages (from-to) | 570-605 |

Number of pages | 36 |

Journal | Nuclear Physics B |

Volume | 890 |

DOIs | |

State | Published - Jan 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics