Quantum Chiral Higher Spin Gravity

TL;DR

This paper presents a consistent four-dimensional flat space higher spin gravity theory that is chiral, exhibits stringy features, and has a trivial S-matrix at all levels, challenging previous no-go theorems.

Contribution

It provides the first explicit example of a quantum interacting higher spin gravity with an action in flat space, demonstrating consistency and vanishing amplitudes.

Findings

Tree-level amplitudes vanish on-shell

Loop corrections also vanish

Full quantum S-matrix is trivial

Abstract

An example of a higher spin gravity in four-dimensional flat space has recently been constructed in arXiv:1609.04655 [hep-th]. This theory is chiral and the action is written in the light-cone gauge. The theory has certain stringy features, e.g. admits Chan-Paton factors. We show that the theory is consistent, both at the classical and quantum level. Even though the interactions are non-trivial, due to the coupling conspiracy all tree level amplitudes vanish on-shell. The loop corrections also vanish. Therefore, the full quantum S-matrix is one and the theory is consistent with the numerous no-go theorems. This provides the first example of a (quantum) interacting higher spin gravity with an action. We argue that higher spin gravities in AdS space should display the same features.