Operator Cutoff Regularization and Renormalization Group in Yang-Mills Theory

TL;DR

This paper develops a gauge-invariant operator cutoff regularization method for Yang-Mills theory, enabling a systematic Wilson-Kadanoff renormalization group analysis that preserves gauge symmetry and accounts for higher dimensional operators.

Contribution

It introduces a novel operator cutoff regularization preserving gauge invariance and derives a renormalization group flow equation incorporating higher dimensional operators in Yang-Mills theory.

Findings

Gauge-invariant low energy effective action derived.

Renormalization group flow equation formulated.

Systematic analysis of higher dimensional operators.

Abstract

We derive a manifestly gauge invariant low energy blocked action for Yang-Mills theory using operator cutoff regularization, a prescription which renders the theory finite with a regulating smearing function constructed for the proper-time integration. By embedding the momentum cutoff scales in the smearing function, operator cutoff formalism allows for a direct application of Wilson-Kadanoff renormalization group to Yang-Mills theory in a completely gauge symmetry preserving manner. In particular, we obtain a renormalization group flow equation which takes into consideration the contributions of higher dimensional operators and provides a systematic way of exploring the influence of these operators as the strong coupling, infrared limit is approached.