The IR sector of QCD: lattice versus Schwinger-Dyson equations

Important information about the infrared dynamics of QCD is encoded in the behavior of its (of-shell) Green's functions, most notably the gluon and the ghost propagators. Due to recent improvements in the quality of lattice data and the truncation schemes employed for the Schwinger-Dyson equations we have now reached a point where the interplay between these two non-perturbative tools can be most fruitful. In this talk several of the above points will be reviewed, with particular emphasis on the implications for the ghost sector, the non-perturbative effective charge of QCD, and the Kugo-Ojima function.Comment: 6 pages. Talk given at QCD@Work 2010 -International Workshop on QCD: Theory and Experiment-, 20-23 June 2010, Martina Franca, Valle d'Itria (Italy

Gauge theories with non-trivial backgrounds

We review our most recent results in formulating gauge theories in the presence of a background field on the basis of symmetry arguments only. In particular we show how one can gain full control over the dependence on the background field of the effective action, and how the so-called background field method emerges naturally from the requirement of invariance under the BRST and antiBRST symmetries.Comment: Contribution to "QCD-TNT-III: From quarks and gluons to hadronic matter: A bridge too far?", 2-6 Sept 2013, ECT*, Trento, Italy; 7 page

Dynamical gluon mass generation and the IR sector of QCD

We review the Pinch Technique - Background Field Method (PT-BFM) framework for formulating and solving the Schwinger-Dyson equations of Yang-Mills theories. In particular, we show how within this framework it is possible to write a new set of Schwinger-Dyson equations that (i) accommodate the dynamical gluon mass generation through Schwinger's mechanism, and (ii) have much better truncation properties than the the conventional equations. The resulting solutions show (in the Landau gauge) an infra-red saturating gluon propagator and ghost dressing function, in agreement with all lattice studies to date for both SU(2) and SU(3) gauge groups as well as 3 and 4 space-time dimensions. We also briefly discuss how a massive gluon enables self-consistently confinement through the condensation of thick vortices, and study other infra-red characteristic quantities such as the Kugo-Ojima function and the effective charge.Comment: 15 pages, 8 figures; plenary talk presented at Light Cone 2010: Relativistic Hadronic and Particle Physics, 14-18 June 2010, Valencia, Spai

Recent results in the infrared sector of QCD

We review the most recent results, derived within the combined framework of the pinch technique and the background field method, describing certain QCD nonperturbative properties.Comment: 8 pages, 3 figures. Talk presented at the International Meeting "Excited QCD", Peniche, Portugal, 6 - 12 May, 201

The two-, three- and four-gluon sector of QCD in the Landau gauge

Due to the nonperturbative masslessness of the ghost field, ghost loops that contribute to gluon Green's functions in the Landau gauge display infrared divergences, akin to those one would encounter in a conventional perturbative treatment. This is in sharp contrast with gluon loops, in which the perturbative divergences are tamed by the dynamical generation of a gluon mass acting as an effective infrared cutoff. In this paper, after reviewing the full nonperturbative origin of this divergence in the two-gluon sector, we discuss its implications for the three- and four-gluon sector, showing in particular that some of the form factors characterizing the corresponding Green's functions are bound to diverge in the infrared.Comment: 13 pages, 7 figures. Talk given at Discrete 2014 - Fourth Symposium on Prospects in the Physics of Discrete Symmetries. 2-6 December, 2014 - King's College, London, Englan

On the dynamics of the Kugo-Ojima function

In this talk, after reviewing the dynamical gluon mass generation mechanism within the pinch technique framework and its phenomenological predictions, we will introduce the modern formulation of the pinch technique which makes extensive use of the Batalin-Vilkovisky quantization formalism. In this framework a certain auxiliary function \Lambda_{\mu\nu}(q) - and its associated form factors G(q^2) and L(q^2) -play a prominent role. After showing that in the (background) Landau gauge \Lambda_{\mu\nu}(q) fully constrains the QCD ghost sector, we show that G(q^2) coincides with the Kugo-Ojima function u(q^2), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. The determination of the behavior of G(q^2) (and therefore of the Kugo-Ojima function) for all momenta through a combination of the available lattice data on the gluon and ghost propagators as well as the dynamical equation G(q^2) satisfies, will be then discussed. In particular we will show that (i) in the deep infrared the function deviates considerably from the value associated with the realization of the Kugo-Ojima confinement scenario, and (ii) establish the dependence on the renormalization point of u(q^2), and especially of its value at q^2=0.Comment: 12 pages, 7 figures. Talk presented at the International Workshop on QCD Green's Functions, Confinement, and Phenomenology - QCD-TNT09, September 07 - 11 2009, ECT* Trento, Ital

IR properties of Yang-Mills theories from the Batalin-Vilkovisky formalism

The powerful quantization formalism of Batalin and Vilkovisky streamlines the derivation of the complete set of (non-linear) identities arising from the local BRST symmetry of Yang-Mills theories. When applied in the Background Field Method type of gauges, it also gives rise to identities which relate Green's functions involving background fields to Green's functions involving quantum fields. All these identities lie at the core of the recent progress in understanding from the continuum formulation the IR dynamics emerging from lattice simulations. In this talk, we will first review the Batalin-Vilkovisky formalism and then apply it to the problem of extracting the effective charge from the available lattice data.Comment: 12 pages, 3 figures. v3: one typo in formula (2.14) corrected. Contribution for the workshop "The many faces of QCD", 1-5 Nov 2010, Ghent, Belgiu

BRST-driven cancellations and gauge invariant Green's functions

We study a fundamental, all order cancellation operating between graphs of distinct kinematic nature, which allows for the construction of gauge-independent effective self-energies, vertices, and boxes at arbitrary order.Comment: 4 pages, 3 figures. Contributed to QCD 03: High-Energy Physics International Conference in Quantum Chromodynamics, Montpellier, France, 2-9 July 200

A dynamical study of the Kugo-Ojima function

As has been recently realized, a certain two-point function $\Lambda$ -- and its associated form factors G and L -- play a prominent role in the PT-BFM formulation of the Schwinger-Dyson equations used to study gauge-invariantly the gluon and ghost propagators. After showing that in the (background) Landau gauge $\Lambda$ fully constrains the QCD ghost sector, we show that G coincides with the Kugo-Ojima function u, whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. The determination of the behavior of G for all momenta through a combination of the available lattice data on the gluon and ghost propagators, as well as the dynamical equation G satisfies, will be then discussed. In particular we will show that in the deep infrared the function deviates considerably from the value associated with the realization of the Kugo-Ojima confinement scenario; the dependence on the renormalization point of u, and especially of its value at q=0, will be also briefly discussed.Comment: 3 pages, 3 figures. Talk presented at the Quark Confinement and the Hadron Spectrum - Madrid 2010, August 30th - September 3rd 2010, Madrid, Spai