The Wilson-Polchinski Renormalization Group Equation in the Planar Limit

TL;DR

This paper derives the Wilson-Polchinski renormalization group equation in the planar limit, revealing its Hamilton-Jacobi structure and incorporating non-planar amplitudes, with applications to various theoretical frameworks.

Contribution

It introduces a Hamilton-Jacobi form of the RG equation in the planar limit, including non-planar sphere topologies, advancing understanding of matrix models and holography.

Findings

RG equation involves non-planar sphere amplitudes

Equation is of Hamilton-Jacobi type

Applications to non-commutative field theories and holography

Abstract

We derive the Wilson-Polchinski RG equation in the planar limit. We explain that the equation necessarily involves also non-planar amplitudes with sphere topology, which represent multi-trace contributions to the effective action. The resulting RG equation turns out to be of the Hamilton-Jacobi type since loop effects manifest themselves through terms which are linear in first order derivatives of the effective action with respect to the sources. We briefly outline applications to renormalization of non-commutative field theories, matrix models with external sources and holography.