arXiv subjects

M. S. Guimaraes

Publications and source records attributed to M. S. Guimaraes.

At least 37 records · Page 2Linked to original sources

arXiv2021

Massive photon propagator in the presence of axionic fluctuations

The theory of massive photons in the presence of axions is studied as the effective theory describing the electromagnetic response of semimetals when a particular quartic fermionic pairing perturbation triggers the formation of charged chiral condensates, giving rise to an axionic superconductor. We investigate corrections to the Yukawa-like potential mediated by massive photons due to axion excitations up to one-loop order and compute the modifications of the London penetration length.

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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.

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arXiv2020

Multivalued fields and monopole operators

In this work, we investigate the role of multivalued fields in the formulation of monopole operators and their connection with topological states of matter. In quantum field theory it is known that certain states describe collective modes of the fundamental fields and are created by operators that are often non-local, being defined over lines or higher-dimensional surfaces. For this reason, they may be sensitive to global, topological, properties of the system and depend on nonperturbative data. Such operators are generally known as monopole operators. Sometimes they act as disorder operators because their nonzero expectation values define a disordered vacuum associated with a condensate of the collective modes, also known as defects. In this work we investigate the definition of these operators and their relation to the multivalued properties of the fundamental fields. We study several examples of scalar field theories and generalize the discussion to $p$-forms, with the main purpose of studying new field configurations that may be related to topological states of matter. We specifically investigate the so-called chiral vortex configurations in topological superconductors. We highlight an important aspect of this formalism, which is the splitting of the fields in their regular and singular parts that identifies an ambiguity that can be explored, much like gauge symmetry, in order to define observables.

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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.

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arXiv2018

Renormalizability of $\mathcal{N}=1$ super Yang-Mills theory in Landau gauge with a Stueckelberg-like field

We construct a vector gauge invariant transverse field configuration $V^H$, consisting of the well-known superfield $V$ and of a Stueckelberg-like chiral superfield. The renormalizability of the Super Yang Mills action in the Landau gauge is analyzed in the presence of a gauge invariant mass term $m^2 \int dV \mathcal{M}(V^H)$, with $\mathcal{M}(V^H)$ a power series in $V^H$. Unlike the original Stueckelberg action, the resulting action turns out to be renormalizable to all orders.

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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.

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arXiv2017

On a renormalizable class of gauge fixings for the gauge invariant operator $A_{\min }^{2}$

The dimension two gauge invariant non-local operator $A_{\min }^{2}$, obtained through the minimization of $\int d^4x A^2$ along the gauge orbit, allows to introduce a non-local gauge invariant configuration $A^h_μ$ which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both $A_{\min }^{2}$ and $A^{h}_μ$ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of $A_{\min }^{2}$ gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as 't Hooft's $R_ζ$-gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field.

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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.

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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.

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arXiv2016

Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory

In this paper, we discuss non-perturbative infrared features of Yang-Mills theory in Euclidean space-time dimensions greater than four in the Landau gauge and within the Refined Gribov-Zwanziger framework, which enables us to take into account the existence of gauge copies by restricting the domain of integration in the path integral to the Gribov region. Evidences for a decoupling/massive solution for the gluon propagator in higher dimensions are provided. This behavior is strengthened the bigger the dimension is. Further, we show that, by a dimensional reduction of the Refined Gribov-Zwanziger action from five to four dimensions, a non-perturbative coupling between the inverse of the Faddeev-Popov operator and the scalar field corresponding to the fifth component of the gauge field naturally arises, being in agreement with the recently proposed mechanism \cite{Capri:2014bsa} to generalize the Refined Gribov-Zwanziger construction to the matter sector.

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arXiv2016

On the gauge-invariant operator $A^2_{\min}$ in Euclidean Yang-Mills theories

We review our recent work on the gauge-invariant non-local dimension-two operator $A^2_{\rm min}$, whose minimization is defined along the gauge orbit. Albeit non-local, the operator $A^2_{\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The whole procedure results into a local action which turns out to be renormalizable to all orders.

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arXiv2016

Effective field theories for superconducting systems with multiple Fermi surfaces

In this work we investigate the description of superconducting systems with multiple Fermi surfaces. For the case of one Fermi surface we re-obtain the result that the superconductor is more precisely described as a topological state of matter. Studying the case of more than one Fermi surface, we obtain the effective theory describing a time reversal symmetric topological superconductor. These results are obtained by employing a general procedure to construct effective low energy actions describing states of electromagnetic systems interacting with charges and defects. The procedure consists in taking into account the proliferation or dilution of these charges and defects and its consequences for the low energy description of the electromagnetic response of the system. We find that the main ingredient entering the low energy characterization of the system with more the one Fermi surface is a non-conservation of the canonical supercurrent triggered by particular vortex configurations.

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arXiv2016

A local and renormalizable framework for the gauge-invariant operator $A^2_{\min}$ in Euclidean Yang-Mills theories in linear covariant gauges

We address the issue of the renormalizability of the gauge-invariant non-local dimension-two operator $A^2_{\rm min}$, whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator $A^2_{\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A^2_{\rm min}$ turns out to be independent from the gauge parameter $α$ entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator $A^2$ in the Landau gauge.

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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.

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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.

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arXiv2016

Confinement and dynamical chiral symmetry breaking in a non-perturbative renormalizable quark model

Inspired by the construction of the Gribov-Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice data. To further validate the physical nature of the model, we identify a massless pseudoscalar (i.e. a pion) in the chiral limit and present estimates for the rho meson mass and decay constant.

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arXiv2015

The Veneziano ghost, glost and gauge copies in QCD

In this short note, we come back to the recent proposal put forward by Kharzeev and Levin [PRL 114 (2015) 24, 242001], in which they phenomenologically couple the non-perturbative Veneziano ghost to the perturbative gluon, leading to a modified gluon propagator (the "glost") of the Gribov type, with complex poles. As such, a possible link was made between the QCD topological θ-vacuum (Veneziano ghost) and color confinement (no physically observable gluons). We discuss some subtleties concerning gauge (BRST) invariance of this proposal, related to the choice of Feynman gauge. We furthermore provide an example in the Landau gauge of a similar phenomenological vertex that also describes the necessary Veneziano ghost but does not affect the Landau gauge gluon propagator.

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arXiv2015

Thermodynamics of an exactly solvable confining quark model

The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a softly BRST-broken version of QCD and possesses a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a nontrivial and stable thermodynamic behaviour at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of nonperturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain nontrivial features, being far away from an ideal gas picture.

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