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David Dudal

Publications and source records attributed to David Dudal.

At least 55 records · Page 3Linked to original sources
arXiv2022

Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball

The estimation of the Källén-Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an appropriate inversion method. As proof of concept the SU(2) glueball spectrum for the quantum numbers $J^{PC} = 0^{++}$ is investigated for various values of the lattice spacing. The spectral density and the glueball spectrum are estimated using the published data of arXiv:1910.07756. Our estimates for the ground state mass are in good agreement with the traditional approach published therein, which is based on the large time exponential behaviour of the correlation functions. Furthermore, the spectral density also contains hints of excites states in the spectrum.

hep-lat↗
arXiv2021

Mass estimates of the SU(2) $0^{++}$ glueball from spectral methods

The estimation of the Källén-Lehmann spectral density from gauge invariant lattice QCD two point correlation functions is proposed, and explored via an inversion strategy based on Tikhonov regularisation. We test the method on a mesonic toy model, showing that our methodology is competitive with the traditional Maximum Entropy Method. As proof of concept the SU(2) glueball spectrum for the quantum numbers $J^{PC}=0^{++}$ is investigated, for various values of the lattice spacing, using the published data of arXiv:1910.07756. Our estimates for the ground state mass are in good agreement with the traditional approach, which is based on the large time exponential behaviour of the correlation functions. Furthermore, the spectral density also contains hints of excites states in the spectrum. Spectroscopic analysis of glueball two-point functions therefore provides a straightforward and insightful alternative to the traditional method based on the large time exponential behaviour of the correlation functions.

hep-lat↗
arXiv2021

Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization

The renormalization properties of two local gauge invariant composite operators $(O,R^a_μ)$ corresponding, respectively, to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are analyzed to all orders in perturbation theory by means of the algebraic renormalization in the $SU(2)$ Higgs model, with a single scalar in the fundamental representation, when quantized in the Landau gauge in Euclidean space-time. The present analysis generalizes earlier results presented in the case of the $U(1)$ Higgs model. A powerful global Ward identity, related to an exact custodial symmetry, is derived for the first time, with deep consequences at the quantum level. In particular, the gauge invariant vector operators $R^a_μ$ turn out to be the conserved Noether currents of the above-mentioned custodial symmetry. As such, these composite operators do not renormalize, as expressed by the fact that the renormalization $Z$-factors of the corresponding external sources, needed to define the operators $R^a_μ$ at the quantum level, do not receive any quantum corrections. Another consistency feature of our analysis is that the longitudinal component of the two-point correlation function $\langle R^a_μ(p) R^b_ν(-p) \rangle$ exhibits only a tree level non-vanishing contribution which, moreover, is momentum independent, being thus not associated to any physical propagating mode. Finally, we point out that the renowned non-renormalization theorem for the ghost-antighost-vector boson vertex in Landau gauge remains true to all orders, also in presence of the Higgs field.

hep-th↗
arXiv2021

Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator

Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation functions within the class of linear covariant gauges. We derive the LKFT for the quark propagator and explicitly evaluate it up to the two loop level in the chiral limit. Although the number of diagrams to be evaluated is significantly larger than with the conventional computational scheme, the diagrams are simpler in nature, thereby leading to a considerably faster evaluation of the gauge dependent part than naively expected. Finally, we also resum the LKFT generated terms and compare our results with earlier work in the literature.

hep-th↗
arXiv2021

Quaternionic Step Derivative: Machine Precision Differentiation of Holomorphic Functions using Complex Quaternions

The known Complex Step Derivative (CSD) method allows easy and accurate differentiation up to machine precision of real analytic functions by evaluating them a small imaginary step next to the real number line. The current paper proposes that derivatives of holomorphic functions can be calculated in a similar fashion by taking a small step in a quaternionic direction instead. It is demonstrated that in so doing the CSD properties of high accuracy and convergence are carried over to derivatives of holomorphic functions. To demonstrate the ease of implementation, numerical experiments were performed using complex quaternions, the geometric algebra of space, and a $2 \times 2$ matrix representation thereof.

math.NA↗
arXiv2021

Chiral transition in the probe approximation from an Einstein-Maxwell-dilaton gravity model

We refine an earlier introduced 5-dimensional gravity solution capable of holographically capturing several qualitative aspects of (lattice) QCD in a strong magnetic background such as the anisotropic behaviour of the string tension, inverse catalysis at the level of the deconfinement transition or sensitivity of the entanglement entropy to the latter. Here, we consistently modify our solution of the considered Einstein-Maxwell-dilaton system to not only overcome an unphysical flattening at large distances in the quark-antiquark potential plaguing earlier work, but also to encapsulate inverse catalysis for the chiral transition in the probe approximation. This brings our dynamical holographic QCD model yet again closer to a stage at which it can be used to predict magnetic QCD quantities not directly computable via lattice techniques.

hep-th↗
arXiv2020

Inversion of electromagnetic induction data using a novel wavelet-based and scale-dependent regularization term

The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and, based on Occam's razor principle, a smoothing constraint is typically used. However, the conductivity profiles are not always expected to be smooth. Here, we develop a new inversion scheme in which we transform the model to the wavelet space and impose a sparsity constraint. This sparsity constrained inversion scheme will minimize an objective function with a least-squares data misfit and a sparsity measure of the model in the wavelet domain. A model in the wavelet domain has both temporal as spatial resolution, and penalizing small-scale coefficients effectively reduces the complexity of the model. Depending on the expected conductivity profile, an optimal wavelet basis function can be chosen. The scheme is thus adaptive. Finally, we apply this new scheme on a frequency domain electromagnetic sounding (FDEM) dataset, but the scheme could equally apply to any other 1D geophysical method.

physics.geo-ph↗
arXiv2020

The Casimir energy in terms of boundary quantum field theory: the QED case

We revisit the path integral computation of the Casimir energy between two infinite parallel plates placed in a QED vacuum. We implement perfectly magnetic conductor boundary conditions (as a prelude to the dual superconductor picture of the QCD vacuum) via constraint fields and show how an effective gauge theory can be constructed for the constraint boundary fields, from which the Casimir energy can be simply computed, in perfect agreement with the usual more involved approaches. Gauge invariance is natural in this framework, as well as the generalization of the result to $d$ dimensions. We also pay attention to the case where the outside of the plates is not the vacuum, but a perfect magnetic (super)conductor, disallowing any dynamics outside the plates. We find perfect agreement between both setups.

hep-th↗
arXiv2020

Landau-Khalatnikov-Fradkin Transformations, Nielsen Identities, Their Equivalence and Implications for QCD

The Landau-Khalatnikov-Fradkin transformations (LKFTs) represent an important tool for probing the gauge dependence of the correlation functions within the class of linear covariant gauges. Recently these transformations have been derived from first principles in the context of non-Abelian gauge theory (QCD) introducing a gauge invariant transverse gauge field expressible as an infinite power series in a Stueckelberg field. In this work we explicitly calculate the transformation for the gluon propagator, reproducing its dependence on the gauge parameter at the one loop level and elucidating the role of the extra fields involved in this theoretical framework. Later on, employing a unifying scheme based upon the BRST symmetry and a resulting generalized Slavnov-Taylor identity, we establish the equivalence between the LKFTs and the Nielsen identities which are also known to connect results in different gauges.

hep-th↗
arXiv2020

Anisotropic string tensions and inversely magnetic catalyzed deconfinement from a dynamical AdS/QCD model

We extend previous work on dynamical AdS/QCD models by introducing an extra ingredient under the form of a background magnetic field, this to gain insight into the influence such field can have on crucial QCD observables. Therefore, we construct a closed form analytic solution to an Einstein-Maxwell-dilaton system with a magnetic field. We specifically focus on the deconfinement transition, reporting inverse magnetic catalysis, and on the string tension, reporting a weaker/stronger confinement along/perpendicular to the magnetic field. The latter, being of importance to potential modelling of heavy quarkonia, is in qualitative agreement with lattice findings.

hep-th↗
arXiv2020

Spectral representation of lattice gluon and ghost propagators at zero temperature

We consider the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space. In order to perform this continuation, the common approach is to first extract the Källén-Lehmann spectral density of the field. Once this is known, it can be extended to Minkowski space to yield the Minkowski propagator. However, obtaining the Källén-Lehmann spectral density from propagator data is a well known ill-posed numerical problem. To regularize this problem we implement an appropriate version of Tikhonov regularization supplemented with the Morozov discrepancy principle. We will then apply this to various toy model data to demonstrate the conditions of validity for this method, and finally to zero temperature gluon and ghost lattice QCD data. We carefully explain how to deal with the IR singularity of the massless ghost propagator. We also uncover the numerically different performance when using two ---mathematically equivalent--- versions of the Källén-Lehmann spectral integral.

hep-lat↗
arXiv2020

A damped forward EMI model for a horizontally stratified earth

If a magnetic dipole is placed above the surface of the earth, the Electromagnetic Induction (EMI) effect, encoded in Maxwell's equations, causes eddy currents in the soil which, on their turn, induce response electromagnetic fields. The magnetic field can be measured in geophysical surveys to determine the conductivity profile of the ground in a non-destructive manner. The forward model used in the inversion of experimental data usually consists of a set of horizontal homogeneous layers. A frequently used analytical model, proposed by McNeill, does not include the interaction between the eddy currents, and therefore fails for larger conductivities. In this paper we construct a new forward, analytical, model to estimate the magnetic field caused by a horizontally stratified earth but which approximates the interaction between eddy currents. This makes it valid for a broader range of parameters than the current state of the art. Furthermore, the error with the (numerically obtainable) exact result is substantially decreased. We also calculate the vertical sensitivity ("depth of exploration") of the model and observe that it is in good agreement with the values obtained from the exact model.

physics.geo-ph↗
arXiv2019

Gauge-invariant spectral description of the $U(1)$ Higgs model from local composite operators

The spectral properties of a set of local gauge-invariant composite operators are investigated in the $U(1)$ Higgs model quantized in the 't Hooft $R_ξ$ gauge. These operators enable us to give a gauge-invariant description of the spectrum of the theory, thereby surpassing certain incommodities when using the standard elementary fields. The corresponding two-point correlation functions are evaluated at one-loop order and their spectral functions are obtained explicitly. As expected, the above mentioned correlation functions are independent from the gauge parameter $ξ$, while exhibiting positive spectral densities as well as gauge-invariant pole masses corresponding to the massive photon and Higgs physical excitations.

hep-th↗
arXiv2019

Extracting topological information from momentum space propagators

A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.

hep-th↗
arXiv2019

Gribov horizon, Polyakov loop and finite temperature

We consider finite-temperature $SU(2)$ gauge theory in the continuum formulation. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy with respect to the Polyakov-loop parameter and solving the Gribov gap equation. The main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. Finally, problems for the pressure at low temperatures are reported.

hep-th↗
arXiv2018

BRST invariant $d=2$ condensates in Gribov-Zwanziger theory

In this proceeding, $SU(N)$ Yang-Mills theory is quantized in the linear covariant gauges, while taking into account the issue of Gribov copies and we construct the one-loop effective potential for a set of mass dimension 2 condensates, including the Gribov parameter, that refines the infrared region of the Gribov-Zwanziger theory, whilst respecting renormalization group invariance and BRST symmetry.

hep-ph↗