How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples

TL;DR

This paper explains the mechanisms of higher-spin gravity, reviews no-go theorems and positive results, and discusses how higher-spin symmetry can be compatible with the equivalence principle in curved backgrounds.

Contribution

It provides a comprehensive overview of no-go theorems and positive results in higher-spin gravity, highlighting how higher-spin symmetry can be integrated with the equivalence principle.

Findings

No-go theorems restrict massless higher-spin interactions in flat spacetime.

Positive cubic higher-derivative vertices exist in curved backgrounds.

Higher-spin gravity can reconcile with the equivalence principle via Fradkin--Vasiliev vertices.

Abstract

Aiming at non-experts, we explain the key mechanisms of higher-spin extensions of ordinary gravity. We first overview various no-go theorems for low-energy scattering of massless particles in flat spacetime. In doing so we dress a dictionary between the S-matrix and the Lagrangian approaches, exhibiting their relative advantages and weaknesses, after which we high-light potential loop-holes for non-trivial massless dynamics. We then review positive yes-go results for non-abelian cubic higher-derivative vertices in constantly curved backgrounds. Finally we outline how higher-spin symmetry can be reconciled with the equivalence principle in the presence of a cosmological constant leading to the Fradkin--Vasiliev vertices and Vasiliev's higher-spin gravity with its double perturbative expansion (in terms of numbers of fields and derivatives).