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

TL;DR

This paper analyzes the Vasiliev higher-spin theory with a strong Sp(2,R) condition, showing it yields correct mass terms and gauge symmetry, and discusses implications for curvature expansion.

Contribution

It introduces a strong Sp(2,R) projection in Vasiliev's construction, clarifying its effects on on-shell constraints and gauge symmetries in higher-spin theories.

Findings

Proper mass terms emerge with the strong Sp(2,R) projection.

The gauge symmetry remains unconstrained and traceful.

Discussion on the finiteness of the curvature expansion.

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.