Gluon Condensation in Nonperturbative Flow Equations

TL;DR

This paper uses nonperturbative flow equations to analyze the effective action in Yang-Mills theories, finding that the true vacuum favors zero magnetic field and indicating gluon condensation with a nonzero field strength expectation value.

Contribution

It introduces a nonperturbative flow equation approach to study the effective action and gluon condensation in Yang-Mills theories, challenging previous perturbative vacuum instability assumptions.

Findings

The effective action minimum occurs at B=0.

Gluon condensation corresponds to a nonzero expectation value of F_{ u}F^{ u}.

Results align with phenomenological estimates.

Abstract

We employ nonperturbative flow equations for an investigation of the effective action in Yang-Mills theories. We compute the effective action $\Gamma[B]$ for constant color magnetic fields $B$ and examine Savvidy's conjecture of an unstable perturbative vacuum. Our results indicate that the absolute minimum of $\Gamma[B]$ occurs for B=0. Gluon condensation is described by a nonvanishing expectation value of the regularized composite operator $F_{\mu\nu}F^{\mu\nu}$ which agrees with phenomenological estimates.