Understanding Higher-Spin Gravity through Bilocal Holography for Free Fermions

We consider a simple theory of N free fermions in d dimensions with O\left(N\right) or U\left(N\right) symmetry. The singlet sector of this theory is expected from holography to be dual to the notoriously complicated Vasiliev gravity. By defining bilocal fields we find an explicit holographic mapping between the two theories, similar to what was done previously for scalars, which allows us to construct a quantum version of Vasiliev gravity, including loop (=1/N) corrections. Further more, such a mapping establishes a non-supersymmetric instance of the AdS/CFT duality.