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We find a geometrical description from a field theoretical setup based onWilson's renormalization group in real space. We show that renormalizationgroup equations of coupling parameters encode the metric structure of anemergent curved space, regarded to be an Einstein equation for the emergentgravity. Self-consistent equations of local order-parameter fields with anemergent metric turn out to describe low energy dynamics of a strongly coupledfield theory, analogous to the Maxwell equation of the Einstein-Maxwell theoryin the AdS$_{d+2}$/CFT$_{d+1}$ duality conjecture. We claim that theAdS$_{3}$/CFT$_{2}$ duality may be interpreted as Landau-Ginzburg theorycombined with Wilson's renormalization group, which introduces vertexcorrections into the Landau-Ginzburg theory in the large$-N_{s}$ limit, where$N_{s}$ is the number of fermion flavors.

Emergent geometry from field theory: Wilson's renormalization group revisited