A local and renormalizable framework for the gauge-invariant operator $A_{\min }^2$ in Euclidean Yang-Mills theories in linear covariant gauges

Abstract

We address the issue of the renormalizability of the gauge-invariant non-local dimension-two operator $A_{\min }^2$, whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator $A_{\min }^2$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A_{\min }^2$ turns out to be independent from the gauge parameter $\alpha$ entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator $A^2$ in the Landau gauge.

35 pages; v2: ref. added

References in corpus (12)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Infrared propagators of Yang-Mills theory from perturbation theory
• Indirect lattice evidence for the Refined Gribov-Zwanziger formalism and the gluon condensate $⟨A^2⟩$ in the Landau gauge
• Covariant gauge on the lattice: a new implementation
• Yang-Mills two-point functions in linear covariant gauges
• On gluon and ghost propagators in linear covariant gauges
• Quantum properties of a non-Abelian gauge invariant action with a mass parameter
• One loop renormalization of the non-local gauge invariant operator min_U (A^U_mu)^2 in QCD
• Unitarity analysis of a non-Abelian gauge invariant action with a mass

Cited by in corpus (4)

• Non-perturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST invariant two-point correlation function
• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• Aspects of the refined Gribov-Zwanziger action in linear covariant gauges
• An all order renormalizable Refined-Gribov-Zwanziger model with BRST invariant fermionic horizon function in linear covariant gauges