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Emergent geometry in recursive renormalization group transformations

Holographic duality conjecture has been proposed to be a novel non-perturbative theoretical framework for the description of strongly correlated electrons. However, the duality transformation is not specified to cause ambiguity in the application of this theoretical machinery to condensed matter physics. In this study, we propose a prescription for the holographic duality transformation. Based on recursive renormalization group (RG) transformations, we obtain an effective field theory, which manifests the RG flow of an effective action through the introduction of an extra dimension. Resorting to this prescription, we show that RG equations of all coupling constants are reformulated as emergent geometry with an extra dimension. We claim that the present prescription serves as microscopic foundation for the application of the holographic duality conjecture to condensed matter physics.