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.

• Received 2 March 2020
• Accepted 13 April 2020

DOI:https://doi.org/10.1103/PhysRevD.101.106001

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Published by the American Physical Society