Higher Spin Gauge Theories: Star-Product and AdS Space

TL;DR

This paper reviews higher spin gauge theories in AdS space, exploring their algebraic structure, solutions, and the relationship between star-products, geometry, and locality, with new results on higher spin currents and solutions.

Contribution

It introduces new solutions to higher spin equations in 4D and generalizes previous 3D results, deepening understanding of higher spin symmetries and their geometric implications.

Findings

Generalized 3D flow to 4D for higher spin equations

Constructed explicit solutions of massless higher spin fields

Analyzed the star-product structure's role in AdS geometry

Abstract

We review the theory of higher spin gauge fields in 2+1 and 3+1 dimensional anti-de Sitter space and present some new results on the structure of higher spin currents and explicit solutions of the massless equations. A previously obtained d=3 integrating flow is generalized to d=4 and is shown to give rise to a perturbative solution of the d=4 nonlinear higher spin equations. A particular attention is paid to the relationship between the star-product origin of the higher spin symmetries, AdS geometry and the concept of space-time locality.