Gluon condensation and scaling exponents for the propagators in Yang-Mills theory

Abstract

We investigate the infrared (strong-coupling) regime of SU($N$)-Yang-Mills theory on a self-dual background. We present an evaluation of the full effective potential for the field-strength invariant ${F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$ from nonperturbative gauge correlation functions and find a nontrivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the $\ensuremath{\beta}$ function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators. Consistency between both gauges in the infrared imposes a new upper bound on the infrared exponents of the propagators. For the scaling solution, this bound reads ${\ensuremath{\kappa}}_{c}l23/38$ which, together with Zwanziger's horizon condition ${\ensuremath{\kappa}}_{c}g1/2$, defines a rather narrow window for this critical exponent. Current estimates from functional methods indeed satisfy these bounds.