An Analytic Yang-Mills Vacuum Calculation in $3+1d$

TL;DR

This paper introduces an analytic method for studying the vacuum structure of 4D $SU(N)$ Yang-Mills theory, incorporating non-perturbative effects to address infrared divergences and evaluate stability claims.

Contribution

It develops a novel analytic framework combining background and effective field techniques to include non-perturbative effects in Yang-Mills vacuum calculations.

Findings

Assessment of Savvidy's IR divergence stabilization claim

Identification of conditions for IR finiteness in Yang-Mills theory

Insights into the role of cubic and quartic interactions in vacuum stability

Abstract

I present a novel analytic framework for $SU(N)$ Yang-Mills theory in the four-dimensional continuum. Background and effective field theory techniques are used to include non-perturbative contributions from cubic and quartic interactions. This approach is inspired by Savvidy who claims first-order contributions from quartic interactions stabilize IR divergence found at one-loop order, making possible IR finite Yang-Mills calculations. I assess the validity of this claim and discuss the implications of my findings.