An exact statement for Wilsonian and Holographic renormalization group

Abstract

We show that Polchinski equations in the D--dimensional matrix scalar field theory can be reduced at large $N$ to the Hamiltonian equations in a (D+1)-dimensional theory. In the subsector of the $\Tr ϕ^l$ (for all $l$) operators we find the exact form of the corresponding Hamiltonian. The relation to the Holographic renormalization group is discussed.

7 pages, no figures, minor changes

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Cited by in corpus (7)

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• Holographic dual of free field theory
• Hints on integrability in the Wilsonian/holographic renormalization group
• Higher Spin vs. Renormalization Group Equations
• Holographic RG flows and boundary conditions in a 3D gauged supergravity
• Moduli Stabilization and the Holographic RG for AdS and dS
• Gradient Flow and Holography from a Local Wilsonian Cutoff