  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.
