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

Background independent holographic description : From matrix field theory to quantum gravity