  We propose a local renormalization group procedure where length scale is
changed in spacetime dependent way. Combining this scheme with an earlier
observation that high energy modes in renormalization group play the role of
dynamical sources for low energy modes at each scale, we provide a prescription
to derive background independent holographic duals for field theories. From a
first principle construction, it is shown that the holographic theory dual to a
D-dimensional matrix field theory is a (D+1)-dimensional quantum theory of
gravity coupled with matter fields of various spins. The gravitational theory
has (D+1) first-class constraints which generate local spacetime
transformations in the bulk. The (D+1)-dimensional diffeomorphism invariance is
a consequence of the freedom to choose different local RG schemes.
