Spectral dimension as a tool for analyzing non-perturbative propagators

Abstract

We derive general properties of the scale-dependent effective spectral dimensions of non-perturbative gauge boson propagators as they appear as solutions from different methods in Yang-Mills theories. In the ultraviolet and for short time scales the anomalous dimensions of the propagators lead to a slight decrease of the spectral dimension as compared to the one of a free propagator. Lowering the momentum scale, the spectral dimension decreases further. The class of propagators which display a maximum at Euclidean momenta, and thus violate positivity, always approaches a spectral dimension of one for large times. We also show that the longest time intervals are not related to the deep infrared but to the momentum scale defined by the position of the maximum.

12 pages, 8 figures; v2: added proofs in App. C, agrees with published version

References in corpus (21)

• 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
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Dimension and Dimensional Reduction in Quantum Gravity
• Spectral functions of confined particles
• On the zero crossing of the three-gluon vertex
• Further Evidence For Zero Crossing On The Three Gluon Vertex
• On gluon and ghost propagators in linear covariant gauges
• Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results
• Alternative refined Gribov-Zwanziger Lagrangian
• On non-primitively divergent vertices of Yang-Mills theory
• Gluon mass scale through nonlinearities and vertex interplay
• The effects of Gribov copies in 2D gauge theories
• Spurious divergences in Dyson-Schwinger equations
• The Gluon Propagator with Two-loop Schwinger-Dyson Equations
• Spectral dimensions from the spectral action
• Running coupling in the conformal window of large-Nf QCD
• Confinement and Green functions in Landau-gauge QCD

Cited by in corpus (8)

• Correlation functions of Landau gauge Yang-Mills theory
• Gluon propagator and three-gluon vertex with dynamical quarks
• Gauge Sector Dynamics in QCD
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
• Novel sum rules for the three-point sector of QCD
• Gluon dynamics from an ordinary differential equation
• $H(4)$ tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts
• Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate