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A. D. Pereira

Publications and source records attributed to A. D. Pereira.

24 records · Page 2Linked to original sources
arXiv2016

Exploring new horizons of the Gribov problem in Yang-Mills theories

The understanding of the non-perturbative regime of YM theories remains a challenging open problem in theoretical physics. Notably, a satisfactory description of the confinement of gluons is not at our disposal so far. In this thesis, the RGZ framework, designed to provide a proper quantization of YM theories by taking into account the existence of the so-called Gribov copies is explored. Successfully introduced in the Landau gauge, the RGZ set up does not extend easily to different gauges. The main reason is that a clear formulation of the analogue of the Gribov horizon in the Landau gauge is obstructed by technical difficulties when more sophisticated gauges are chosen. Moreover, the RGZ action breaks BRST symmetry explicitly, making the task of extracting gauge invariant results even more difficult. The main goal of the present thesis is precisely to provide a consistent framework to extend the RGZ action to gauges that are connected to Landau gauge via a gauge parameter. Our main result is the reformulation of the theory in the Landau gauge with appropriate variables such that a non-perturbative BRST symmetry is constructed. This symmetry corresponds to a deformation of the standard BRST symmetry by taking into account non-perturbative effects. This opens a toolbox which allow us to explore what would be the Gribov horizon in different gauges as linear covariant and Curci-Ferrari gauges. Consistency with gauge independence of physical quantities as well as the computation of the gluon propagator in these gauges is provided. Remarkably, when lattice or functional methods results are available, we verify very good agreement with our analytical proposal giving support that it could provide some insights about the non-perturbative regime of YM theories. A positivity violating gluon propagator in the infrared seems to be a general feature of the formalism.

hep-th↗
arXiv2016

Gauges and functional measures in quantum gravity I: Einstein theory

We perform a general computation of the off-shell one-loop divergences in Einstein gravity, in a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family of gauges. Trying to reduce the gauge- and measure-dependence selects certain classes of measures and gauges respectively. There is a choice of two parameters (corresponding to the exponential parametrization and the partial gauge condition that the quantum field be traceless) that automatically eliminates the dependence on the remaining two parameters and on the cosmological constant. We observe that the divergences are invariant under a $\mathbf{Z}_2$ "duality" transformation that (in a particularly important special case) involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable. This singles out a formulation of unimodular gravity as the unique "self-dual" theory in this class.

hep-th↗
arXiv2016

A local and BRST-invariant Yang-Mills theory within the Gribov horizon

We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies à la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.

hep-th↗
arXiv2016

More on the non-perturbative Gribov-Zwanziger quantization of linear covariant gauges

In this paper, we discuss the gluon propagator in the linear covariant gauges in $D=2,3,4$ Euclidean dimensions. Non-perturbative effects are taken into account via the so-called Refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for $D=3,4$, the gluon propagator displays a massive (decoupling) behaviour, while for $D=2$, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced non-perturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our non-perturbative definition of the linear covariant gauge.

hep-th↗
arXiv2015

Non-perturbative treatment of the linear covariant gauges by taking into account the Gribov copies

In this paper, a proposal for the restriction of the Euclidean functional integral to a region free of infinitesimal Gribov copies in linear covariant gauges is discussed. An effective action, akin to the Gribov-Zwanziger action of the Landau gauge, is obtained which implements the aforementioned restriction. Although originally non-local, this action can be cast in local form by introducing auxiliary fields. As in the case of the Landau gauge, dimension two condensates are generated at the quantum level, giving rise to a refinement of the action which is employed to obtain the tree-level gluon propagator in linear covariant gauges. A comparison of our results with those available from numerical lattice simulations is also provided.

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