Background Independent Holographic Description : From Matrix Field Theory to Quantum Gravity

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A local renormalization group procedure is proposed where length scale is changed in spacetime dependent manner. 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 (D+1)-dimensional diffeomorphism invariance is a consequence of the freedom to choose different local RG schemes.