Bosonic Higher Spin Gravity in any Dimension with Dynamical Two-Form

TL;DR

This paper introduces an alternative bosonic higher spin gravity model in any dimension, utilizing a modified gauge algebra and a superconnection framework, which may unify various deformations and gauge conditions into a single variational principle.

Contribution

It proposes a new higher spin gravity model with a modified gauge algebra, embedding it into a superconnection, and unifies gauge conditions into a Frobenius-Chern-Simons action.

Findings

Perturbative equivalence with Vasiliev's model at linear level

Embedding into a superconnection with additional degrees of freedom

Unification of gauge conditions into a single flatness condition

Abstract

We first propose an alternative to Vasiliev's bosonic higher spin gravities in any dimension by factoring out a modified sp(2) gauge algebra. We evidence perturbative equivalence of the two models, which have the same spectrum of Fronsdal fields at the linearized level. We then embed the new model into a flat Quillen superconnection containing two extra master fields in form degrees one and two; more generally, the superconnection contains additional degrees of freedom associated to various deformations of the underlying non-commutative geometry. Finally, we propose that by introducing first-quantized sp(2) ghosts and duality extending the field content, the Quillen flatness condition can be unified with the sp(2) gauge conditions into a single flatness condition that is variational with a Frobenius-Chern-Simons action functional.