Geometry and Observables in Vasiliev's Higher Spin Gravity

We provide global formulations of Vasiliev's four-dimensional minimal bosonic higher spin gravities by identifying structure groups, soldering one-forms and classical observables. In the unbroken phase, we examine how decorated Wilson loops collapse to zero-form charges and exploit them to enlarge the Vasiliev system with new interactions. We propose a metric phase whose characteristic observables are minimal areas of higher spin metrics and on shell closed abelian forms of positive even degrees. We show that the four-form is an on shell deformation of the generalized Hamiltonian action recently proposed by Boulanger and one of the authors. In the metric phase, we also introduce tensorial coset coordinates and demonstrate how single derivatives with respect to coordinates of higher ranks factorize into multiple derivatives with respect to coordinates of lower ranks.