Exact Renormalization Group and Loop Equation

TL;DR

This paper introduces a gauge invariant exact renormalization group formulation for pure Yang-Mills theory that connects to loop equations and has potential implications for holography.

Contribution

It presents a novel gauge invariant RG equation for Yang-Mills theory that relates to loop equations and Schwinger-Dyson equations, extending previous work.

Findings

RG equation is a regularized loop equation

Establishes a connection between RG and Schwinger-Dyson equations

Discusses implications for holographic duality

Abstract

We propose a gauge invariant formulation of the exact renormalization group equation for nonsupersymmetric pure U(N) Yang-Mills theory, based on the construction by Tim Morris. In fact we show that our renormalization group equation amounts to a regularized version of the loop equation, thereby providing a direct relation between the exact renormalization group and the Schwinger-Dyson equations. We also discuss a possible implication of our formulation to the holographic correspondence of the bulk gravity and the boundary gauge theory.