An exact statement for Wilsonian and Holographic renormalization group

TL;DR

This paper demonstrates that Polchinski equations in large N matrix scalar field theory can be reformulated as Hamiltonian equations in a higher-dimensional space, establishing a precise connection to the Holographic renormalization group.

Contribution

It provides an exact Hamiltonian form of the Polchinski equations at large N and clarifies their relation to the Holographic renormalization group.

Findings

Reduction of Polchinski equations to Hamiltonian form at large N

Explicit Hamiltonian for operators Tr φ^l

Discussion of the relation to Holographic RG

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 $\Tr \phi^l$ (for all $l$) operators we find the exact form of the corresponding Hamiltonian. The relation to the Holographic renormalization group is discussed.