  The Quantum renormalization group (QRG) is a realisation of holography
through a coarse graining prescription that maps the beta functions of a
quantum field theory thought to live on the `boundary' of some space to
holographic actions in the `bulk' of this space. A consistency condition will
be proposed that translates into general covariance of the gravitational theory
in the $D + 1$ dimensional bulk. This emerges from the application of the QRG
on a planar matrix field theory living on the $D$ dimensional boundary. This
will be a particular form of the Wess--Zumino consistency condition that the
generating functional of the boundary theory needs to satisfy. In the bulk,
this condition forces the Poisson bracket algebra of the scalar and vector
constraints of the dual gravitational theory to close in a very specific
manner, namely, the manner in which the corresponding constraints of general
relativity do. A number of features of the gravitational theory will be fixed
as a consequence of this form of the Poisson bracket algebra. In particular, it
will require the metric beta function to be of gradient form.
