Doubletons and 5D Higher Spin Gauge Theory

TL;DR

This paper constructs a bosonic higher spin gauge theory in five dimensions by introducing the hs(2,2) algebra as a coset of a oscillator–based structure and identifying its spectrum with the symmetric product of two spin-0 doubletons. The authors define master fields A and Phi, along with a master scalar field, and derive linearized curvature and scalar constraints that reproduce the massless higher spin equations for spins s=0,2,4,... around AdS$_5$. The central generator K is factored out to remove degeneracies, and the resulting spectrum forms a unitary irrep of hs(2,2). The work lays the groundwork for an interacting theory whose AdS curvature expansion would be dual to a boundary CFT built from free doubletons in the large N limit, suggesting a truncation of tensionless Type IIB string theory on $AdS_5\times S^5$. It further points to possible supersymmetric extensions and connections to broader M-theory contexts.

Abstract

We use Grassmann even spinor oscillators to construct a bosonic higher spin extension hs(2,2) of the five-dimensional anti-de Sitter algebra SU(2,2), and show that the gauging of hs(2,2) gives rise to a spectrum S of physical massless fields with spin s=0,2,4,... that is a UIR of hs(2,2). In addition to a master gauge field which contains the massless s=2,4,.. fields, we construct a scalar master field containing the massless s=0 field, the generalized Weyl tensors and their derivatives. We give the appropriate linearized constraint on this master scalar field, which together with a linearized curvature constraint produces the correct linearized field equations. A crucial step in the construction of the theory is the identification of a central generator K which is eliminated by means of a coset construction. Its charge vanishes in the spectrum S, which is the symmetric product of two spin zero doubletons. We expect our results to pave the way for constructing an interacting theory whose curvature expansion is dual to a CFT based on higher spin currents formed out of free doubletons in the large N limit. Thus, extending a recent proposal of Sundborg (hep-th/0103247), we conjecture that the hs(2,2) gauge theory describes a truncation of the bosonic massless sector of tensionless Type IIB string theory on AdS_5 x S^5 for large N. This implies AdS/CFT correspondence in a parameter regime where both boundary and bulk theories are perturbative.