Propagators approximated by a meromorphic functions with complex conjugated poles are widely used to model infrared behavior of QCD Green's functions. In this paper, analytical solutions for two point correlator made out of functions with complex conjugated poles or branch points have been obtained in the Minkowski space for the first time. As a special case the Gribov propagator has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. It is free of ultraviolet divergences, and instead of Lehmann it rather satisfies Gribov integral representation.
The aim of this paper is to present a connection between the Gribov-Zwanziger condition for the mass gap and spontaneous symmetry breaking. In order to clarify these relationship a toy model is presented and quantum aspects are discussed.
During recent years, a good agreement was found between the analytical derivation and the numerical simulation of the Landau gauge gluon and ghost propagators. We mention the Schwinger-Dyson and Gribov-Zwanziger formalism for the analytical work. Although the agreement between several approaches is nice, these propagators do not correspond to the relevant physical degrees of freedom. In the case of pure gauge theories, one should start to study the glueball correlators. We shall try to explain why it looks like a hard challenge to go from the unphysical to the physical propagators in the case …
Over the last years, lattice calculations in pure Yang-Mills gauge theory seem to have come more or less to a consensus. The ghost propagator is not enhanced and the gluon propagator is positivity violating, infrared suppressed and non-vanishing at zero momentum. From an analytical point of view, several groups are agreeing with these results. Among them, the refined Gribov-Zwanziger (RGZ) framework also accommodates for these results. The question which rises next is, if our models hold the right form for the propagators, how to extract information on the real physical observables, i.e. the g…
We reexamine the conventional arguments concerned with the scaling and decoupling solutions for the ghost and gluon propagators in the Landau gauge Yang-Mills theory. We point out a few issues to be clarified, which seems to be overlooked in the previous investigations in this field, in the fully non-perturbative treatment. We propose a trick which enables one to incorporate the Gribov horizon directly into the self-consistent Schwinger-Dyson equation in the gauge-fixed Yang-Mills theory, using the Gribov-Zwanziger framework with the horizon term. We obtain the following results, irrespective …
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 Gribov's no-pole condition, can be implemented by demanding a nonvanishing expectation value f…
In this paper the Gribov gap equation at finite temperature is analyzed. The solutions of the gap equation (which depend explicitly on the temperature) determine the structure of the gluon propagator within the semi-classical Gribov approach. The present analysis is consistent with the standard confinement scenario for low temperatures, while for high enough temperatures, deconfinement takes place and a free gluon propagator is obtained. It also suggests the presence of the so-called semi-quark-gluon-plasma phase in between the confined and quark-gluon plasma phases.
In this work we study the behaviour of Yang--Mills--Chern--Simons theory coupled to a Higgs field in the fundamental representation by taking into account the effects of the presence of the Gribov horizon. By analyzing the infrared structure of the gauge field propagator, both confined and de-confined regions can be detected. The confined region corresponds to the appearance of complex poles in the propagators, while the de-confined one to the presence of real poles. One can move from one region to another by changing the parameters of the theory.
The quantization of Yang-Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider in particular the SU (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass…
The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates
The present work discusses an approach to access the physical spectrum of the Yang-Mills theory quantized in the Landau gauge. By using recent lattice data on the gluon propagator, it is possible to study the two-point functions of gauge invariant composite operators, from which masses of glueballs can be extracted. It turns out that the momentum dependence of the gluon propagator is very well reproduced by the corresponding tree-level gluon propagator obtained from the Refined Gribov-Zwanziger theory, which takes into account the presence of the Gribov horizon as well as the effect of condens…
The low momentum behavior of the Landau gauge Gribov-Zwanziger action is investigated using the respective Dyson-Schwinger equations. Because of the mixing of the gluon and the auxiliary fields four scenarios can be distinguished for the infrared behavior. Two of them lead to inconsistencies and can be discarded. Another one corresponds to the case where the auxiliary fields behave exactly like the Faddeev-Popov ghosts and the same scaling relation as in standard Landau gauge, $\ka_A+2\ka_c=0$, is valid. Even the parameter $\ka$ is found to be the same, 0.595. The mixed propagators, which appe…
This Ph.D. thesis presents a study of the Gribov-Zwanziger framework: from propagators to glueballs. The chapters 2 and 3 are meant as an introduction and only require a basic knowledge of quantum field theory. Chapter 2 explains the techniques behind algebraic renormalization, which shall be widely used throughout this thesis, while chapter 3 tries to give a pedagogic overview of the Gribov-Zwanziger framework as this is not available yet in the literature. The subsequent chapters contain own research. First in chapter 4, we shall dig a bit deeper in the Gribov-Zwanziger framework, by explori…
We study the structure of the gauge propagators of a 3d version of the electroweak interaction in terms of the Higgs vacuum expectation value nu, of the non-Abelian gauge coupling g, and of the Abelian gauge coupling g', when nonperturbative effects related to the non-Abelian gauge fixing are introduced by means of an adapted path integral measure. In the perturbative regime of small non-Abelian coupling g and sufficiently large nu, the well-known standard Z and W propagators are recovered, together with a massless photon. In general, depending on the relative magnitudes of g, g' and nu, we un…
We consider the implications of the condensation of a general local BRST invariant dimension two operator built out of the localizing ghost fields of the Gribov-Zwanziger Lagrangian which is a localized Lagrangian incorporating the Gribov problem in the Landau gauge. For different colour tensor projections of the general operator, the properties of a frozen gluon propagator and unenhanced Faddeev-Popov ghost propagator, which are observed in lattice computations, can be reproduced. The alternative possibilities are distinguished by the infrared structure of the propagators of the spin-1 fields…
The construction of BRST invariant local operators with the quantum numbers of the lightest glueball states, $J^{PC}= 0^{++}, 2^{++}, 0^{-+}$, is worked out by making use of an Euclidean confining renormalizable gauge theory. The correlation functions of these operators are evaluated by employing a confining gluon propagator of the Gribov type and shown to display a spectral representation with positive spectral densities. An attempt to provide a first qualitative analysis of the ratios of the masses of the lightest glueballs is also discussed
The compatibility of the results from the Gribov-Zwanziger tree level prediction and lattice simulations, using large statistical ensembles, for the Landau gauge gluon propagator are investigated, thereby complementing earlier work using small-scale statistics. Our results show that the data is well described by the tree level estimate only up to momenta $p \lesssim 1$ GeV while clearly favoring the so-called Refined Gribov-Zwanziger scenario, implying particular relations between certain possible $d=2$ condensates. We also provide a global fit of the lattice data which interpolates between th…
It is known that Noncommutative QED (NCQED) exhibits Gribov ambiguities in the Landau gauge. These ambiguities are related to zero modes of the Faddeev-Popov operator and arise in the ghost propagator when it has a pole. In this work, we establish a positive Faddeev-Popov operator for NCQED and the condition for the ghost propagator not to have poles, the so-called Gribov no-pole condition. This condition is implemented in the path integral, and allows for the calculation of the photon propagator in momentum space, which is dependent on the squared non-commutativity parameter. In the commutati…
We compute the two loop corrections to the gluon propagator for low momentum in a gluon mass model. This model has recently been proposed as an alternative to the Gribov construction in the way it handles Gribov copies in the gauge fixing. The corrections provide improvements for estimating the point where the gluon propagator freezes in relation to lattice data.
In this work, we study the propagators of matter fields within the framework of the Refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the Refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST invariant formulation of the Gribov-Zwanziger framework achieved in [Capri et al 2016], the propagators of scalar and quark fields in the adjoi…
We introduce, within the Refined-Gribov-Zwanziger setup, a composite BRST invariant fermionic operator coupled to the inverse of the Faddeev-Popov operator. As a result, an effective BRST invariant action in Euclidean space-time is constructed, enabling us to pave the first step towards the study of the behaviour of the fermion propagator in the infrared region in the class of the linear covariant gauges. The aforementioned action is proven to be renormalizable to all orders by means of the algebraic renormalization procedure.
As the restriction of the gauge fields to the Gribov region is taken into account, it turns out that the resulting gauge field propagators display a nontrivial infrared behavior, being very close to the ones observed in lattice gauge field theory simulations. In this work, we explore for the first time a higher correlation function in the presence of the Gribov horizon: the ghost-anti-ghost-gluon interaction vertex, at one-loop level. Our analytical results (within the so-called Refined Gribov Zwanziger theory) are fairly compatible with lattice YM simulations, as well as with solutions from t…
We construct the local Gribov-Zwanziger action for SU(2) Euclidean Yang-Mills theories in the maximally Abelian (MA) gauge with U(1)$_3$ Landau gauge fixing based on the Zwanziger's work in the Landau gauge. By the restriction of the functional integral region to the Gribov region in the MA gauge, we give the nonlocal action. We localize the action with new fields and obtain the action with the shift of the new scalar fields, which has the terms, corresponding to the localized action of the horizon function in the MA gauge. The diagonal gluon propagator in the MA gauge at tree level behaves li…
We present an analytical study of continuum 4d SU(2) gauge Higgs models with a single Higgs field with fixed length in either the fundamental or adjoint representation. We aim at analytically probing the renowned predictions of Fradkin & Shenker on the phase diagram in terms of confinement versus Higgs behaviour, obtained for the lattice version of the model. We work in the Landau version of the 't Hooft R_ξgauges in which case we can access potential nonperturbative physics related to the existence of the Gribov copies. In the fundamental case, we clearly show that in the perturbative regime …
We explore a contact point between two distinct approaches to the confinment problem. We show that BLG-ABJM like theories generate gauge propagators with just the complex pole structure prescribed by the Gribov scenario for confinemnt. This structure, known as i-particles in Gribov-Zwanziger theories, effectively allows the definition of composite operators with a positive Källén-Lehmann spectral representation for their two-point functions . Then, these operators satisfy the criteria to describe glue-ball condensates. We calculate the (first order) contribution to the two-point function of th…
We rewrite the Zwanziger horizon condition in terms of the Kugo-Ojima parameter for color confinement. This enables one to explain which value of the Kugo-Ojima parameter is allowed if the horizon condition is imposed. Although all the calculations are performed in the limit of vanishing Gribov parameter for simplicity, the obtained value is consistent with the result of numerical simulations. Consequently, the ghost propagator behaves like free and the gluon propagator is non-vanishing at low momenta, in harmony with recent lattice results and decoupling solution of the Schwinger-Dyson equati…
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 simply adding a gluon mass term to the usual Faddeev-Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in good 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…
Recent works have explored non-perturbative effects due to the existence of (infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three Euclidean dimensions. In particular, the removal of such copies modify the gauge field propagator by a self-consistent dynamically generated mass parameter, the Gribov parameter. Due to the interplay with the topological mass introduced by the Chern-Simons term, the propagator features a non-trivial set of phases with poles of different nature, leading to the possible interpretation of a confinfing to deconfining phase transition. Inhere, we res…
We study the Landau-gauge Gribov ghost form-factor sigma(p^2) for SU(N) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d=3,4 w.r.t. d=2. In particular, considering any (sufficiently regular) gluon propagator D(p^2) and the one-loop-corrected ghost propagator G(p^2), we prove in the 2d case that sigma(p^2) blows up in the infrared limit p -> 0 as -D(0)\ln(p^2). Thus, for d=2, the no-pole condition σ(p^2) < 1 (for p^2 > 0) can be satisfied only if D(0) = 0. On the contrary, in d=3 and 4, sigma(p^2) is finite also if D(0) > 0. The same results are ob…
We consider the gluon propagator $D(p^2)$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (Refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate $\braket{A^2}$. Including this effect allows to obtain an acceptable fit up to 1 á 1.5 GeV, while corroborating the Refined Gribov-Zwanziger prediction for …
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 functiona…
We prove that the Faddeev-Popov ghost dressing function in the Yang-Mills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the $D$-dimensional SU(N) Yang-Mills theory in the Landau gauge for any $D>2$. This result implies that the Kugo-Ojima color confinement criterion is not satisfied in its original form. We point out that the result crucially depends on the explicit form of the non-local horizon term adopted. The original Gribov prediction in the Landau gauge…
Propagator positivity bounds for cosmological correlators
Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（国立台湾大学梁中心宇宙学与粒子天体物理学）；Department of Physics and Astronomy, Queen Mary University of London（伦敦玛丽女王大学物理与天文系）
The infrared behavior of propagators and vertices is derived for the maximally Abelian gauge and the Gribov-Zwanziger action relying on functional equations. The derivation and analysis of Dyson-Schwinger equations increase considerably in complexity when going beyond the standard Landau gauge fixing and the available tools have to be improved. For the derivation of the equations a computer program (DoDSE) was developed in order to handle the plethora of terms. The process of determining possible infrared solutions is abstracted to obtain further insight into the structure of the so-called inf…
We explore whether a tree-level expression for the gluon two-point function, supposed to express effects of an horizon term introduced to eliminate the Gribov ambiguity, is consistent with the propagator obtained in simulations of lattice-regularised quantum chromodynamics (QCD). In doing so, we insist that the gluon two-point function obey constraints that ensure a minimal level of consistency with parton-like behaviour at ultraviolet momenta. In consequence, we are led to a position which supports a conjecture that the gluon mass and horizon scale are equivalent emergent mass-scales, each wi…
We derive a gauge-invariant low-energy effective model of the Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type and agrees with it when a mass term which breaks nilpotency of the BRST symmetry is included. We show that the effective model with gluon propagator of the Gribov-Stingl type exhibits both quark and gluon confinement: the Wilson loop average has the area law and the Schwinger function violates reflection positivity. However, we argue that both quark and gluon confinement can be obtained even in the absence of such a mass term.
We have computed in [arXiv:1107.4320 (hep-th)] the glueballs spectrum in a certain sector of the large-N YM theory by solving by a change of variables the holomorphic loop equation for cusped twistor Wilson loops supported on certain Lagrangian submanifolds and by evaluating the correlators of surface operators supported on these Lagrangian submanifolds. We have shown that the correlators of composite surface operators of length L reproduce in the large-L limit the leading logarithms of perturbation theory of the corresponding glueballs propagators, including the correct anomalous dimensions. …
