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We investigate the infrared (strong-coupling) regime of SU(N)-Yang-Millstheory on a self-dual background. We present an evaluation of the fulleffective potential for the field strength invariant F_{\mu {\nu}}F^{\mu {\nu}}from non-perturbative gauge correlation functions and find a non-trivialminimum corresponding to the existence of a dimension four gluon condensate inthe vacuum. We also relate the infrared asymptotic form of the beta function ofthe running background-gauge coupling to the asymptotic behavior ofLandau-gauge gluon and ghost propagators. Consistency between both gauges inthe infrared imposes a new upper bound on the infrared exponents of thepropagators. For the scaling solution, this bound reads kappa_c < 23/38 which,together with Zwanziger's horizon condition kappa_c> 1/2, defines a rathernarrow window for this critical exponent. Current estimates from functionalmethods indeed satisfy these bounds.

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