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

TL;DR

This paper explores the non-perturbative infrared behavior of SU(N)-Yang-Mills theory, revealing a gluon condensate and establishing bounds on propagator exponents through effective potential analysis and gauge correlation functions.

Contribution

It provides a non-perturbative evaluation of the effective potential and derives new bounds on the infrared exponents of gluon and ghost propagators in Yang-Mills theory.

Findings

Identification of a non-trivial gluon condensate in the vacuum.

Derivation of bounds on the infrared exponents of propagators.

Consistency established between different gauge approaches.

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_{\mu {\nu}}F^{\mu {\nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the 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 kappa_c < 23/38 which, together with Zwanziger's horizon condition kappa_c> 1/2, defines a rather narrow window for this critical exponent. Current estimates from functional methods indeed satisfy these bounds.