Quantum Chiral Higher Spin Gravity

TL;DR

The paper constructs a four-dimensional, chiral higher spin gravity in the light-cone gauge with Chan-Paton factors and shows it is consistent both classically and quantum mechanically. The main result is that all tree-level amplitudes vanish on-shell due to a coupling conspiracy and that loop corrections cancel, yielding a quantum S-matrix equal to unity: $S=1$. This provides the first explicit example of a quantum interacting HiSGRA with an explicit action and suggests that AdS HiSGRA counterparts may display similar UV behavior. The work also connects to holographic perspectives via dual free CFTs and situates these results within broader contexts of self-dual and conformal higher spin theories.

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.