Faddeev-Popov Action Research Articles

Exploiting the scheme dependence of the renormalization group improvement in infrared Yang–Mills theory

Within the refined Gribov–Zwanziger scenario for four-dimensional Yang–Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that adding a gluon mass term to the usual Faddeev–Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in reasonable agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization scheme dependence can be used to achieve an almost perfect matching to the lattice data for the gluon and ghost propagators.

A note on Faddeev-Popov action for doubled-yet-gauged particle and graded Poisson geometry

The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev-Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which might be comparable with the Fradkin-Tseytlin term on string worldsheet.

Two-loop calculation of Yang-Mills propagators in the Curci-Ferrari model

The Landau-gauge gluon and ghost correlation functions obtained in lattice simulations can be reproduced qualitatively and, to a certain extent, quantitatively if a gluon mass is added to the standard Faddeev-Popov action. This has been tested extensively at one loop, for the two and three point correlation functions of the gluons, ghosts and quarks. In this article, we push the comparison to two loops for the gluon and ghost propagators. The agreement between lattice results and the perturbative calculation considerably improves. This validates the Curci-Ferrari action as a good phenomenological model for describing the correlation functions of Yang-Mills theory in the Landau gauge. It also indicates that the perturbation theory converges fairly well, in the infrared regime.

A note on unfree gauge symmetry

We study the general structure of field theories with the unfree gauge symmetry where the gauge parameters are restricted by differential equations. The examples of unfree gauge symmetries include volume preserving diffeomorphisms in the unimodular gravity and various higher spin field theories with transverse gauge symmetries. All the known examples of the models with unfree gauge symmetry share one common feature. They admit local quantities which vanish on shell, though they are not linear combinations of Lagrangian equations and their derivatives. We term these quantities as mass shell completion functions.In the case of usual gauge symmetry with unconstrained gauge parameters, the irreducible gauge algebra involves the two basic constituents: the action functional and gauge symmetry generators. For the case of unfree gauge symmetry, we identify two more basic constituents: operators of gauge parameter constraints and completion functions. These two extra constituents are involved in the algebra of unfree gauge symmetry on equal footing with action and gauge symmetry generators.Proceeding from the algebra, we adjust the Faddeev-Popov (FP) path integral quantization scheme to the case of unfree gauge symmetry. The modified FP action involves the operators of the constraints imposed on the gauge parameters, while the corresponding BRST transformation involves the completion functions. The BRST symmetry ensures gauge independence of the path integral. We provide two examples which admit the alternative unconstrained parametrization of gauge symmetry and demonstrate that they lead to the equivalent FP path integral.

Construction of a massive ABJM theory without Higgs superfields

A massive Aharony-Bergman-Jafferis-Maldacena (ABJM) model in superspace is analysed by considering a Proca-type mass term into the most general Faddeev-Popov action in a covariant gauge. The presence of a mass term breaks the original BRST and anti-BRST invariance of the model. Further, the symmetry of the massive ABJM model is restored by extending the BRST and anti-BRST transformations. We show that the supergauge dependence of the generating functional for connected diagrams occurs in the presence of mass and ghost–anti-ghost condensates in the theory.

Three-point correlation functions in Yang-Mills theory

We investigate the three-point correlation functions of Yang-Mills theory in the Landau gauge, with a particular emphasis on the infrared regime. The effect of the Gribov copies is accounted for by adding a mass term for the gluons in the Faddeev-Popov action in the Landau gauge. We perform a one-loop calculation for the ghost-antighost-gluon and three-gluon correlation functions. These analytic results are compared with the available lattice data and give a very satisfying agreement.

Lifting the Gribov ambiguity in Yang–Mills theories

We propose a new one-parameter family of Landau gauges for Yang–Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Faddeev–Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Faddeev–Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some – including physically relevant – range of values of the renormalized parameters.

Infrared safe perturbative approach to Yang-Mills correlators

We investigate the 2-point correlation functions of Yang-Mills theory in the Landau gauge by means of a massive extension of the Faddeev-Popov action. This model is based on some phenomenological arguments and constraints on the ultraviolet behavior of the theory. We show that the running coupling constant remains finite at all energy scales (no Landau pole) for $d>2$ and argue that the relevant parameter of perturbation theory is significantly smaller than 1 at all energies. Perturbative results at low orders are therefore expected to be satisfactory and we indeed find a very good agreement between 1-loop correlation functions and the lattice simulations, in 3 and 4 dimensions. Dimension 2 is shown to play the role of an upper critical dimension, which explains why the lattice predictions are qualitatively different from those in higher dimensions.

Gluon confinement, i-particles and BRST soft breaking

A few issues on gluon confinement are addressed with the help of a renormalizable gauge model obtained by introducing a replica of the Faddeev–Popov action and a soft breaking of the BRST symmetry. Confinement turns out to be encoded in the spectral properties of the corresponding correlation functions. While the propagators of the elementary fields have no interpretation in terms of physical excitations, examples of local composite operators whose two-point correlation functions possess a spectral representation with positive spectral density can be introduced. These composite operators turn out to be left invariant by the BRST transformations, a feature which has strong consequences on their renormalizability properties. Moreover, they display a direct interpretation in terms of i-particles (Baulieu et al 2010 Phys. Rev. D 82 025021), which are the unphysical modes corresponding to a confining propagator of the Gribov type. A possible way to take into account the effects of the Gribov copies is also outlined.

Infrared propagators of Yang-Mills theory from perturbation theory

We show that the correlation functions of ghosts and gluons for the pure Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta by a one-loop calculation. The key point is to use a massive extension of the Faddeev-Popov action. The agreement with lattice simulation is excellent in d=4. The one-loop calculation also reproduces all the characteristic features of the lattice simulations in d=3 and naturally explains the pecularities of the propagators in d=2.

Action from the Gribov horizon

The euclidean action of gauge theories is derived here, taking due account of the restriction of the physical configuration space to the interior of the Gribov horizon. This adds a new term to the Faddeev-Popov action. In a model defined by a simple approximation to the action, the new term is found to have little effect on high momentum components of the gauge field, but it strongly suppresses low momentum components, so that the gluon propagator in the Landau gauge vanishes at low momentum like k 2.

Supersymmetric quantization of linearized supergravity

We give a manifestly supersymmetric quantization scheme for linearized supergravity, motivated by the desire to develop a background field method for the full non-linear theory. Supersymmetric gauge-fixing constraints are constructed and the corresponding ghost action is discussed. It is found that the Faddeev-Popov action itself possesses invariances, requiring “secondary” gauge fixing, which in turn leads to “secondary” ghost fields, the latter having normal statistics. The gauge-fixing constraints are used to construct gauge-fixing terms in the action, with a total of four gauge-fixing parameters. The superpropagators are found and may be greatly simplified by certain choices of these parameters.