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

Sudarshan Fernando, Murat Günaydin

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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 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.

Original languageEnglish (US)
Pages (from-to)570-605
Number of pages36
JournalNuclear Physics B
Volume890
DOIs
StatePublished - Jan 1 2015

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All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

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