On Exact Solutions and Perturbative Schemes in Higher Spin Theory

TL;DR

This paper reviews methods for finding exact solutions in higher spin theory, surveys known solutions, and discusses perturbative schemes and geometric descriptions to better understand the structure of Vasiliev's equations.

Contribution

It introduces and compares two perturbative schemes for solving Vasiliev's equations and revisits a geometric framework for higher spin invariants.

Findings

Survey of known exact solutions including instanton-like and black hole-like configurations.

Development of two perturbative solution schemes for Vasiliev's equations.

Improved geometric approach for higher spin invariant characterization.

Abstract

We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev's equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is described as well. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green's functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev's equation involving an infinite dimensional generalization of anti de Sitter space is revisited and improved.