Higher-spin dynamics and Chern-Simons theories

TL;DR

This paper reviews the construction of higher-spin theories using Chern-Simons actions, focusing on algebraic structures, curvature tensors, and perturbative analysis in five dimensions to derive four-dimensional equations.

Contribution

It introduces higher-spin algebras, discusses curvature tensors unconstrained, and performs a perturbative analysis to connect five-dimensional Chern-Simons theories with four-dimensional higher-spin equations.

Findings

Derived four-dimensional Fronsdal equations from five-dimensional Chern-Simons theory.

Presented a perturbative approach in a non-maximally symmetric AdS background.

Clarified the algebraic and geometric foundations of higher-spin Chern-Simons theories.

Abstract

We review the construction of consistent higher-spin theories based on Chern-Simons actions. To this end we first introduce the required higher-spin algebras and discuss curvature and torsion tensors in an unconstrained way. Finally we perform a perturbative analysis of the Chern-Simons theory in D=5 for a non-maximally symmetric AdS(4) background and obtain the required four-dimensional Fronsdal equations in the compensator formulation.