Doubletons and 5D Higher Spin Gauge Theory

TL;DR

This paper constructs a five-dimensional higher spin gauge theory using Grassmann spinor oscillators, identifying its spectrum and constraints, and discusses its potential duality with a conformal field theory in the context of AdS/CFT correspondence.

Contribution

It introduces a new bosonic higher spin extension hs(2,2) of the AdS_5 algebra, detailing the spectrum, gauge fields, and constraints, and proposes its connection to tensionless string theory and dual CFTs.

Findings

Constructed the hs(2,2) algebra using Grassmann oscillators.

Identified the spectrum as a symmetric product of doubletons.

Proposed a duality with a large N limit of free doubleton CFTs.

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.