M. S. Guimaraes

Glueball Masses from an Infrared Moment Problem

We set up an infrared-based moment problem to obtain estimates of the masses of the scalar, pseudoscalar, and tensor glueballs in Euclidean Yang-Mills theories using the refined Gribov-Zwanziger (RGZ) version of the Landau gauge, which takes into account nonperturbative physics related to gauge copies. Employing lattice input for the mass scales of the RGZ gluon propagator, the lowest order moment problem approximation gives the values m(0++) ≈ 1.96 GeV, m(2++) ≈ 2.04 GeV, and m(0-+) ≈ 2.19 GeV in the SU(3) case, all within a 20% range of the corresponding lattice values. We also recover the mass hierarchy m(0++) < m(2++) < m(0-+).

Exact nilpotent nonperturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge

We point out the existence of a nonperturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.

Study of the properties of the Gribov region in SU(N) Euclidean Yang–Mills theories in the maximal Abelian gauge

In this paper we address the issue of the Gribov copies in SU(N), N > 2, Euclidean Yang–Mills theories quantized in the maximal Abelian gauge. A few properties of the Gribov region in this gauge are established. Similar to the case of SU(2), the Gribov region turns out to be convex, bounded along the off-diagonal directions in field space, and unbounded along the diagonal ones. The implementation of the restriction to the Gribov region in the functional integral is discussed through the introduction of the horizon function, whose construction will be outlined in detail. The influence of this restriction on the behavior of the gluon and ghost propagators of the theory is also investigated together with a set of dimension 2 condensates.

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 a 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.

An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions

Abstract The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev–Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU ( N ) Yang–Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribovʼs no-pole condition, can be implemented by demanding a non-vanishing expectation value for a functional of the gauge fields that turns out to be Zwanzigerʼs horizon function. The action allowing to implement this condition is the Gribov–Zwanziger action. This establishes in a precise way the equivalence between Gribovʼs no-pole condition and Zwanzigerʼs horizon condition.

Implementing the Gribov–Zwanziger framework in \(\mathcal {N}=1\) Super-Yang–Mills in the Landau gauge

The Gribov–Zwanziger framework accounting for the existence of Gribov copies is extended to

Properties of the Faddeev-Popov operator in the Landau gauge, matter confinement and soft BRST breaking

\mathcal {N}=1

Padé approximation and glueball mass estimates in 3d and 4d with Nc = 2, 3 colors

N=1 Super-Yang–Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of