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

TL;DR

The paper addresses the challenge of formulating interacting massless higher-spin gauge theories in four-dimensional spacetime by reviewing no-go theorems that forbid such interactions in flat space and outlining viable escape routes. It centers on the Fradkin–Vasiliev mechanism in AdS, where the cosmological constant plays a dual role as infrared and derivative regulator, and on Vasiliev’s unfolded equations as a fully nonlinear realization. Through S-matrix no-go results, Lagrangian cubic vertices, and AdS/CFT insights, the authors map the landscape of possible higher-spin interactions, highlighting the tension between locality, higher-derivative couplings, and gauge symmetry. The work suggests that a complete higher-spin gravity framework, especially in AdS, can provide a consistent quantum gravity scenario with deep connections to holography and tensionless string ideas, while also outlining key open problems such as quartic-order consistency and the infrared behavior of the coupling.

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).