Minimal unitary representation of 5d superconformal algebra F(4) and AdS_6/CFT_5 higher spin (super)-algebras

TL;DR

This paper constructs minimal unitary representations of the 5d superconformal algebra F(4) and explores their extensions to higher spin AdS_6/CFT_5 superalgebras, revealing their algebraic structures and physical interpretations.

Contribution

It introduces the minimal unitary representations of SO(5,2) and F(4), and extends these to higher spin AdS_6/CFT_5 superalgebras using quasiconformal methods.

Findings

Minreps describe massless conformal fields in five dimensions.

The enveloping algebra yields higher spin algebras with vanishing Joseph ideal.

Constructed the unique higher spin AdS_6/CFT_5 superalgebra.

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 5d analogs of Dirac's singletons of SO(3,2). We then construct the minimal unitary representation of the unique 5d superconformal algebra F(4) with the even subalgebra SO(5,2) X 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.