On Higher Spins with a Strong Sp(2,R) Condition

TL;DR

This work analyzes Vasiliev’s minimal bosonic higher-spin equations in AdS using a strong Sp(2,R) projection on the 0-form and a weak constraint on the 1-form. It shows that the linearized on-shell system acquires correct mass terms and a geometric gauge symmetry with unconstrained, traceful parameters, while exposing subtleties of the strong projection and the need for a finite curvature expansion. The authors introduce dressing functions M(K^2) and F(N;K^2) that implement the projection and generate a controlled curvature expansion, and they reveal a mixing phenomenon between higher-spin Weyl tensors and lower-level fields that can be diagonalized by a Weyl rescaling, connecting to compensator formulations. They discuss two prospective finite-expansion schemes (minimal and modified) and illustrate key ideas in a simpler U(1) analogue, suggesting a path toward a consistent, finite higher-spin theory with tensionless-string/brane motivations and links to Francia–Sagnotti compensator equations.

Abstract

We report on an analysis of the Vasiliev construction for minimal bosonic higher-spin master fields with oscillators that are vectors of SO(D-1,2) and doublets of Sp(2,R). We show that, if the original master field equations are supplemented with a strong Sp(2,R) projection of the 0-form while letting the 1-form adjust to the resulting Weyl curvatures, the linearized on-shell constraints exhibit both the proper mass terms and a geometric gauge symmetry with unconstrained, traceful parameters. We also address some of the subtleties related to the strong projection and the prospects for obtaining a finite curvature expansion.