Callan-Symanzik approach to infrared Yang-Mills theory

Abstract

Abstract. Dyson-Schwinger equations are the most common tool for the determination of the correlation functions of Landau gauge Yang-Mills theory in the continuum, in particular in the infrared regime. We shall argue that the use of Callan-Symanzik renormalization group equations has distinctive advantages over the Dyson-Schwinger equations, in particular for the vertex functions. We present a generalization of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011. The comparison with the existing lattice data for the gluon and ghost propagators can be used to determine the most appropriate renormalization scheme.Dyson-Schwinger equations have given access to the deep infrared (IR) regime of Landau gauge Yang-Mills theory. The first solutions found show a scaling behavior of the propagators in the IR [1]. Several years later, another type of solutions of the same equations was discovered [2], with a massive gluon propagator and a finitely enhanced ghost propagator in the IR (decoupling solutions). To date, Dyson-Schwinger equations are still the main tool for the (semi-)analytical exploration of the IR regime of Yang-Mills theory.In a parallel development that actually initiated much earlier with Gribov's observation of the existence of gauge copies in his famous 1978 paper [3] and was later worked out in great detail by Zwanziger [4], the theoretical foundations of IR Yang-Mills theory were laid. While this so-called Gribov-Zwanziger scenario seemed to confirm the existence of the scaling solutions, a more recent refinement [5] favors the decoupling type of solutions. Finally, the results of simulations of YangMills theory in the Landau gauge on huge lattices [6] have been interpreted by most workers in the field as confirming the realization of the decoupling type of solutions in three and four space-time dimensions.In this contribution, we will present a different technique for the exploration of the IR regime of Yang-Mills theory. We intend to reproduce the results of lattice simulations in the Landau gauge that restrict the gauge field configurations to the (first) Gribov region, but make no attempt to reach the fundamental modular region. The restriction to the Gribov region implies the breaking of BRST invariance in the continuum formulation [4]. The most important consequence of the broken BRST invariance for the IR regime is the appearance of a mass term for the gluon field [5]. Indeed, the addition of a gluonic mass term to the Yang-Mills action has been shown to reproduce all the solutions (two types of scaling solutions and the decoupling solution) found before with the help of DysonSchwinger equations when solving the Callan-Symanzik equations for this theory in the IR regime in a Speaker,

Modeling the Landau-gauge ghost propagator in 2, 3, and 4 spacetime dimensions

“…( 59) and using the 4d one-loop expression for σ(p 2 ), as well as the fitting function W (p 2 ), defined in Eq. (60). With the values…”

“…1 The interested reader should see Refs. [53][54][55][56][57][58][59][60][61][62][63] for other approaches and points of view on the scaling and/or the massive solutions. 2 Let us mention that this proposed behavior for the gluon propagator, i.e.…”

One-loop unquenched three-gluon vertex in the Curci-Ferrari model

“…Probably the most interesting aspect of this model is the fact that, as it has been shown in various previous articles (see [41,42,49,50,77] for instance), the addition of a gluon mass term regularizes the theory in the infrared, allowing for a perturbative treatment of the theory in this region. More specifically, it is possible to find a renormalization scheme without an infrared Landau pole for particular choices of the initial condition of the renormalization-group flow.…”

On the contribution of different coupling constants in the infrared regime of Yang–Mills theory: A Curci–Ferrari approach

“…The field renormalization factors are defined in the scheme presented in [37], which is a reformulation of the IS-scheme of [26]. In this renormalization scheme, renormalization factors for the fields and the gluon mass respect the conditions:…”