An example of a higher spin gravity in four-dimensional flat space has recently been constructed by D. Ponomarev and E. D. Skvortsov, J. Phys. A, 50, 095401(2017). 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 nontrivial, 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 anti–de Sitter space should display the same features.

Chiral higher spin gravity is unique in being the smallest higher spin extension of gravity and in having a simple local action both in flat and (anti-)de Sitter spaces. It must be a closed subsector of any other higher spin theory in four dimensions, which makes it an important building block and benchmark. Using the flat space version for simplicity, we perform a thorough study of quantum corrections in chiral theory, which strengthens our earlier results [E. Skvortsov, T. Tran, and M. Tsulaia, Phys. Rev. Lett. 121, 031601 (2018)]. Even though the interactions are naively nonrenormalizable, we show that there are no UV divergences in two-, three-, and four-point amplitudes at one loop thanks to the higher spin symmetry. We also give arguments that the AdS chiral theory should exhibit similar properties. It is shown that chiral theory admits Yang-Mills gaugings with $U(N)$, $SO(N)$, and $USp(N)$ groups, which is reminiscent of the Chan-Paton symmetry in string theory.

An example of a consistent theory with massive higher spin fields is constructed in flat space-time of dimension three. The action is written in the light-cone gauge. The theory has certain stringlike features, e.g., its spectrum is unbounded in spin and mass; the theory admits Chan-Paton factors. The quartic and the higher tree-level amplitudes vanish, which softens the UV behavior at the loop level and provides a new mechanism of how massive higher spin states can resolve the quantum gravity problem.

Scattering of two Kerr Black Holes emitting gravitational waves can be captured by an effective theory of a massive higher-spin field interacting with the gravitational field. While other compact objects should activate a multitude of non-minimal interactions it is the black holes that should be captured by the simplest minimal interaction. Implementing massive higher-spin symmetry via a string-inspired BRST approach we construct an action that reproduces the correct cubic amplitude of Arkani-Hamed-Huang-Huang. The same is achieved for the root-Kerr theory, i.e. for the minimal electromagnetic interaction of a massive higher-spin field.

We study quantum properties of supersymmetric $$ \mathcal{N} $$N = 1 and $$ \mathcal{N} $$N = 4 extensions of the four dimensional bosonic Chiral Higher Spin Gravities (HiSGRAs). We discuss the spectra, the classical actions and define the Feynman rules in $$ \mathcal{N} $$N = 1 and $$ \mathcal{N} $$N = 4 superspaces in the light-front gauge. Using these Feynman rules, we compute tree and one-loop amplitudes for these systems. A dimensional reduction to a system with $$ \mathcal{N} $$N = 2 supersymmetry and with massive higher spin fields is performed and quantum properties of this system are discussed.

We give an introduction to the so-called tensorial, matrix or hyperspace approach to the description of massless higher-spin fields.