arXiv subjects

D. Dudal

Publications and source records attributed to D. Dudal.

At least 19 recordsLinked to original sources

arXiv2022

Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement

We consider a BRST invariant generalization of the "massive background Landau gauge", resembling the original Curci-Ferrari model that saw a revived interest due to its phenomenological success in modeling infrared Yang-Mills dynamics, including that of the phase transition. Unlike the Curci-Ferrari model, however, the mass parameter is no longer a phenomenological input but it enters as a result of dimensional transmutation via a BRST invariant dimension two gluon condensate. The associated renormalization constant is dealt with using Zimmermann's reduction of constants program which fixes the value of the mass parameter to values close to those obtained within the Curci-Ferrari approach. Using a self-consistent background field, we can include the Polyakov loop and probe the deconfinement transition, including its interplay with the condensate and its electric-magnetic asymmetry. We report a continuous phase transition at Tc ~ 0.230 GeV in the SU(2) case and a first order one at Tc ~ 0.164 GeV in the SU(3) case, values which are again rather close to those obtained within the Curci-Ferrari model at one-loop order.

hep-th↗

arXiv2022

Half-integer anomalous currents in 2D materials from a QFT viewpoint

Charge carriers in Dirac/Weyl semi-metals exhibit a relativistic-like behavior. In this work we propose a novel type of intrinsic half-integer Quantum Hall effect in 2D materials, thereby also offering a topological protection mechanism for the current. Its existence is rooted in the 2D parity anomaly, without any need for a perpendicular magnetic field. We conjecture that it may occur in disturbed honeycomb lattices where both spin degeneracy and time reversal symmetry are broken. These configurations harbor two distinct gap-opening mechanisms that, when occurring simultaneously, drive slightly different gaps in each valley, causing a net anomalous conductivity when the chemical potential is tuned to be between the distinct gaps. Some examples of promising material setups that fulfill the prerequisites of our proposal are also listed to motivate looking for the effect at the numerical and experimental level.

cond-mat.mes-hall↗

arXiv2021

The Abelian Higgs model under a gauge invariant looking glass: exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem

The content of two additional Ward identities exhibited by the $U(1)$ Higgs model is exploited. These novel Ward identities can be derived only when a pair of local composite operators providing a gauge invariant setup for the Higgs particle and the massive vector boson is introduced in the theory from the beginning. Among the results obtained from the above mentioned Ward identities, we underline a new exact relationship between the stationary condition for the vacuum energy, the vanishing of the tadpoles and the vacuum expectation value of the gauge invariant scalar operator. We also present a characterization of the two-point correlation function of the composite operator corresponding to the vector boson in terms of the two-point function of the elementary gauge fields. Finally, a discussion on the connection between the cartesian and the polar parametrization of the complex scalar field is presented in the light of the Equivalence Theorem. The latter can in the current case be understood in the language of a constrained cohomology, which also allows to rewrite the action in terms of the aforementioned gauge invariant operators. We also comment on the diminished role of the global $U(1)$ symmetry and its breaking.

hep-th↗

arXiv2021

A quenched 2-flavour Einstein-Maxwell-dilaton gauge-gravity model

We extend earlier work by introducing an Einstein-Maxwell-dilaton (EMD) action with two quark flavours. We solve the corresponding equations of motion in the quenched approximation (probe quark flavours) via the potential reconstruction method in presence of a background magnetic field in search for a self-consistent dual magnetic AdS/QCD model. As an application we discuss the deconfinement transition temperature confirming inverse magnetic catalysis, whilst for moderate values of the magnetic field also the entropy density compares relatively well with corresponding lattice data in the vicinity of the transition.

hep-th↗

arXiv2020

Spectral properties of local gauge invariant composite operators in the $SU(2)$ Yang--Mills--Higgs model

The spectral properties of a set of local gauge (BRST) invariant composite operators are investigated in the $SU(2)$ Yang--Mills--Higgs model with a single Higgs field in the fundamental representation, quantized in the 't Hooft $R_ξ$-gauge. These operators can be thought of as a BRST invariant version of the elementary fields of the theory, the Higgs and gauge fields, with which they share a gauge independent pole mass. The two-point correlation functions of both BRST invariant composite operators and elementary fields, as well as their spectral functions, are investigated at one-loop order. It is shown that the spectral functions of the elementary fields suffer from a strong unphysical dependence from the gauge parameter $ξ$, and can even exhibit positivity violating behaviour. In contrast, the BRST invariant local operators exhibit a well defined positive spectral density.

hep-th↗

arXiv2020

Infinitesimal Gribov copies in gauge-fixed topological Yang-Mills theories

We study the Gribov problem in four-dimensional topological Yang-Mills theories following the Baulieu-Singer approach in the (anti-)self-dual Landau gauges. This is a gauge-fixed approach that allows to recover the topological spectrum, as first constructed by Witten, by means of an equivariant (or constrained) BRST cohomology. As standard gauge-fixed Yang-Mills theories suffer from the gauge copy (Gribov) ambiguity, one might wonder if and how this has repercussions for this analysis. The resolution of the small (infinitesimal) gauge copies, in general, affects the dynamics of the underlying theory. In particular, treating the Gribov problem for the standard Landau gauge condition in non-topological Yang-Mills theories strongly affects the dynamics of the theory in the infrared. In the current paper, although the theory is investigated with the same gauge condition, the effects of the copies turn out to be completely different. In other words: in both cases, the copies are there, but the effects are very different. As suggested by the tree-level exactness of the topological model in this gauge choice, the Gribov copies are shown to be inoffensive at the quantum level. To be more precise, following Gribov, we discuss the path integral restriction to the Gribov horizon. The associated gap equation, which fixes the so-called Gribov parameter, is however shown to only possess a trivial solution, making the restriction obsolete. We relate this to the absence of radiative corrections in both gauge and ghost sectors. We give further evidence by employing the renormalization group which shows that, for this kind of topological model, the gap equation indeed forbids the introduction of a massive Gribov parameter.

hep-th↗

arXiv2019

Some remarks on the spectral functions of the Abelian Higgs Model

We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model.

hep-th↗

arXiv2019

The BRST-invariant vacuum state of the Gribov-Zwanziger theory

We revisit the effective action of the Gribov-Zwanziger theory, taking into due account the BRST symmetry and renormalization (group invariance) of the construction. We compute at one loop the effective potential, showing the emergence of BRST-invariant dimension 2 condensates stabilizing the vacuum. This paper sets the stage at zero temperature, and clears the way to studying the Gribov-Zwanziger gap equations, and particularly the horizon condition, at finite temperature in future work.

hep-th↗

arXiv2018

On the exact quantum scale invariance of three-dimensional reduced QED theories

An effective quantum field theory description of graphene in the ultra-relativistic regime is given by reduced QED aka. pseudo QED aka. mixed-dimensional QED. It has been speculated in the literature that reduced QED constitutes an example of a specific class of hard-to-find theories: an interacting CFT in more than two dimensions. This speculation was based on two-loop perturbation theory. Here, we give a proof of this feature, namely the exact vanishing of the b-function, thereby showing that reduced QED can effectively be considered as an interacting (boundary) CFT, underpinning recent work in this area. The argument, valid for both two- and four-component spinors, also naturally extends to an exactly marginal deformation of reduced QED, thence resulting in a non-supersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces.

hep-th↗

arXiv2018

Comments on the Chern-Simons photon term in the QED description of graphene

We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this non-local but still gauge invariant theory, we can confirm that the topological piece of the photon self-energy at zero momentum does not receive further quantum corrections apart from the potential one-loop contribution, even when considering the Lorentz non-invariant case due to the Fermi velocity $v_F<c$. This is of relevance to probe possible time parity odd dynamics in a planar sheet of graphene which has an effective description in terms of $(2+1)$-dimensional planar reduced QED.

hep-th↗

arXiv2018

The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories

In light of the recently established BRST invariant formulation of the Gribov-Zwanziger theory, we show that Zwanziger's horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evaluated with the Yang-Mills action supplemented with a BRST invariant version of the Zwanziger's horizon function and quantized in an arbitrary class of covariant, color invariant and renormalizable gauges which reduce to the Landau gauge when all gauge parameters are set to zero, have a unique, gauge parameters independent result, corresponding to that of the Landau gauge when the restriction to the Gribov region $Ω$ in the latter gauge is imposed. As such, thanks to the BRST invariance, the cut-off at the Gribov region $Ω$ acquires a gauge independent meaning in the class of the physical correlators.

hep-th↗

arXiv2018

Gauge copies in the Landau-DeWitt gauge: a background invariant restriction

The Landau background gauge, also known as the Landau-DeWitt gauge, has found renewed interest during the past decade given its usefulness in accessing the confinement-deconfinement transition via the vacuum expectation value of the Polyakov loop, describable via an appropriate background. In this Letter, we revisit this gauge from the viewpoint of it displaying gauge (Gribov) copies. We generalize the Gribov-Zwanziger effective action in a BRST and background invariant way; this action leads to a restriction on the allowed gauge fluctuations, thereby eliminating the infinitesimal background gauge copies. The explicit background invariance of our action is in contrast with earlier attempts to write down and use an effective Gribov-Zwanziger action. It allows to address certain subtleties arising in these earlier works, such as a spontaneous and thus spurious Lorentz symmetry breaking, something which is now averted.

hep-th↗

arXiv2018

A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.

hep-th↗

arXiv2017

Accessing the topological susceptibility via the Gribov horizon

The topological susceptibility, $χ^4$, following the work of Witten and Veneziano, plays a key role in identifying the relative magnitude of the $η^{\prime}$ mass, the so-called $U(1)_{A}$ problem. A nonzero $χ^4$ is caused by the Veneziano ghost, the occurrence of an unphysical massless pole in the correlation function of the topological current. In a recent paper (Phys.Rev.Lett.114 (2015) 24, 242001), an explicit relationship between this Veneziano ghost and color confinement was proposed, by connecting the dynamics of the Veneziano ghost, and thus the topological susceptibility, with Gribov copies. However, the analysis is incompatible with BRST symmetry (Phys.Rev.D 93 (2016) no.8, 085010). In this paper, we investigate the topological susceptibility, $χ^4$, in SU(3) and SU(2) Euclidean Yang-Mills theory using an appropriate Padé approximation tool and a non-perturbative gluon propagator, within a BRST invariant framework and by taking into account Gribov copies in a general linear covariant gauge.

hep-ph↗

arXiv2017

Double non-perturbative gluon exchange: an update on the soft Pomeron contribution to pp scattering

We employ a set of recent, theoretically motivated, fits to non-perturbative unquenched gluon propagators to check in how far double gluon exchange can be used to describe the soft sector of pp scattering data (total and differential cross section). In particular, we use the refined Gribov--Zwanziger gluon propagator (as arising from dealing with the Gribov gauge fixing ambiguity) and the massive Cornwall-type gluon propagator (as motivated from Dyson-Schwinger equations) in conjunction with a perturbative quark-gluon vertex, next to a model based on the non-perturbative quark-gluon Maris-Tandy vertex, popular from Bethe-Salpeter descriptions of hadronic bound states. We compare the cross sections arising from these models with "older" ISR and more recent TOTEM and ATLAS data. The lower the value of total energy \sqrt{s}, the better the results appear to be.

hep-ph↗

arXiv2017

Gluon and Ghost Dynamics from Lattice QCD

The two point gluon and ghost correlation functions and the three gluon vertex are investigated, in the Landau gauge, using lattice simulations. For the two point functions, we discuss the approach to the continuum limit looking at the dependence on the lattice spacing and volume. The analytical structure of the propagators is also investigated by computing the corresponding spectral functions using an implementation of the Tikhonov regularisation to solve the integral equation. For the three point function we report results when the momentum of one of the gluon lines is set to zero and discuss its implications.

hep-lat↗

arXiv2016

Non-perturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST invariant two-point correlation function

In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use to probe the pole structure of the massive gauge boson in a gauge invariant fashion.

hep-th↗

arXiv2016

Gluons at finite temperature

The gluon propagator is investigated at finite temperature via lattice simulations. In particular, we discuss its interpretation as a massive-type bosonic propagator. Moreover, we compute the corresponding spectral density and study the violation of spectral positivity. Finally, we explore the dependence of the gluon propagator on the phase of the Polyakov loop.

hep-lat↗