Universality From Very General Nonperturbative Flow Equations in QCD

TL;DR

This paper develops a gauge-invariant, exact diagrammatic framework within nonperturbative renormalization group equations in QCD, enabling analysis of gauge-invariant operators without approximations, advancing nonperturbative understanding.

Contribution

It introduces a universal, exact diagrammatic expression for gauge-invariant operators in QCD using general flow equations, avoiding approximations and non-universal details.

Findings

Derived a gauge-invariant exact expression for operator expectation values

Established a nonperturbative framework applicable to general QCD problems

Provided a new approach for analyzing nonperturbative phenomena in gauge theories

Abstract

In the context of very general exact renormalization groups, it will be shown that, given a vertex expansion of the Wilsonian effective action, remarkable progress can be made without making any approximations. Working in QCD we will derive, in a manifestly gauge invariant way, an exact diagrammatic expression for the expectation value of an arbitrary gauge invariant operator, in which many of the non-universal details of the setup do not explicitly appear. This provides a new starting point for attacking nonperturbative problems.