Minimal unitary representation of 5d superconformal algebra F(4)F(4) and AdS6/CFT5AdS6/CFT5 higher spin (super)-algebras

We study the minimal unitary representation (minrep) of SO(5,2)SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2)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)SO(5,2) are the 5d   analogs of Dirac's singletons of SO(3,2)SO(3,2). We then construct the minimal unitary representation of the unique 5d   superconformal algebra F(4)F(4) with the even subalgebra SO(5,2)×SU(2)SO(5,2)×SU(2). The minrep of F(4)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/CFT5AdS6/CFT5 (super)-algebras. The Joseph ideal of the minrep of SO(5,2)SO(5,2) vanishes identically as operators and hence its enveloping algebra yields the AdS6/CFT5AdS6/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/CFT5AdS6/CFT5 superalgebra as the enveloping algebra of the minimal unitary realization of F(4)F(4) obtained by the quasiconformal methods.