Modern Approaches to Non-Perturbative QCD and other Confining Gauge Theories

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Foundations of Quantum Mechanics and Quantum Gravity".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 21009

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Special Issue Editor

Formerly at Departamento de Física and CFIF, Instituto Superior Técnico, ULisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Interests: theoretical high-energy physics and quantum field theory; non-perturbative approaches to quantum chromodynamics: confining strings and their phenomenological applications; models of confinement and chiral-symmetry breaking; thermodynamics and transport properties of strongly interacting quark–gluon plasma; topological and finite-temperature properties of field-theoretical models admitting an analytic description of confinement; effects of confinement in one-loop amplitudes

Special Issue Information

Dear Colleagues,

Since the mid 70s, confinement and chiral-symmetry breaking have been recognized as the main non-perturbative phenomena in quantum chromodynamics (QCD). Yet, their full quantitative description is still lacking. The primary intention of this Special Issue is to provide a collection of reviews on modern approaches to these two phenomena.

In the case of confinement, such approaches include the various microscopic models of the Yang–Mills vacuum, specifically calorons and center vortices, as well as their phenomenological application to the SU(2) Yang–Mills thermodynamics and to the determination of the static potential in the SU(2) QCD with light quarks, respectively. Other microscopic models of confinement, such as those based on the condensation of magnetic monopoles in theories with the compact Abelian gauge group, admit an analytic derivation of the corresponding confining-string action. One of the reviews in this Special Issue is planned to be devoted to the recent studies of confining strings and the application of the related techniques to the analysis of the novel superinsulating state, which emerges in such condensed-matter systems as the Josephson junction arrays.

Furthermore, there exist indications of an interrelation between confinement and chiral-symmetry breaking, which stem, e.g., from the relations between the chiral and the gluon condensates, known from the QCD sum rules and the low-energy QCD theorems. This Special Issue will present a review of an approach to the study of this interrelation by means of lattice simulations of low-lying Dirac eigenmodes. While these modes are delocalised at low temperature, they become localised at high temperature, with the lattice simulations suggesting that the localisation occurs precisely at the deconfinement critical temperature.

A complementary review, devoted to confinement and chiral-symmetry breaking at finite baryon density, will also be presented. The corresponding studies are motivated by the fact that current and planned experiments have the capability to explore the phase diagram of strong interactions. Finite baryon density can affect the possible interplay between confinement and chiral-symmetry breaking, as seen, e.g., in the recently discovered inhomogeneous phases, which may have various confining and topological properties.

Last but not least, one of the reviews presented in this Special Issue will provide an overview of the modern analytic and lattice approaches to confinement.

Dr. Dmitry Antonov
Guest Editor

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Keywords

  • modern analytic and lattice approaches to the problem of quark confinement
  • semiclassical models of the Yang–Mills vacuum (calorons, monopoles, center vortices) and their phenomenological applications (e.g., to the thermodynamics of gluon plasma)
  • confining strings and flux tubes in gauge theories and condensed-matter systems
  • spontaneous breaking of chiral symmetry in QCD and the low-energy spectrum of the QCD Dirac operator
  • the QCD phase diagram and the effects of finite baryon density

Published Papers (12 papers)

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Editorial

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4 pages, 172 KiB  
Editorial
Modern Approaches to Non-Perturbative QCD and Other Confining Gauge Theories
Universe 2022, 8(1), 49; https://doi.org/10.3390/universe8010049 - 13 Jan 2022
Cited by 1 | Viewed by 874
Abstract
The primary goal of this Special Issue was to create a collection of reviews on the modern approaches to the problem of quark confinement in QCD [...] Full article

Research

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17 pages, 1548 KiB  
Article
Local Correlation among the Chiral Condensate, Monopoles, and Color Magnetic Fields in Abelian Projected QCD
Universe 2021, 7(9), 318; https://doi.org/10.3390/universe7090318 - 28 Aug 2021
Cited by 4 | Viewed by 1200
Abstract
Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of (1) a static monopole–antimonopole pair and (2) a magnetic flux without [...] Read more.
Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of (1) a static monopole–antimonopole pair and (2) a magnetic flux without monopoles, on a four-dimensional Euclidean lattice. In these systems, we calculate the local chiral condensate on quasi-massless fermions coupled to the Abelian gauge field, and find that the chiral condensate is localized in the vicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlo calculations, we investigate Abelian projected QCD in the maximally Abelian gauge, and find clear correlation of distribution similarity among the local chiral condensate, monopoles, and color magnetic fields in the Abelianized gauge configuration. As a statistical indicator, we measure the correlation coefficient r, and find a strong positive correlation of r0.8 between the local chiral condensate and an Euclidean color-magnetic quantity F in Abelian projected QCD. The correlation is also investigated for the deconfined phase in thermal QCD. As an interesting conjecture, like magnetic catalysis, the chiral condensate is locally enhanced by the strong color-magnetic field around the monopoles in QCD. Full article
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27 pages, 1398 KiB  
Article
Axial Anomaly in Galaxies and the Dark Universe
Universe 2021, 7(6), 198; https://doi.org/10.3390/universe7060198 - 13 Jun 2021
Cited by 6 | Viewed by 3161
Abstract
Motivated by the SU(2)CMB modification of the cosmological model ΛCDM, we consider isolated fuzzy-dark-matter lumps, made of ultralight axion particles whose masses arise due to distinct SU(2) Yang–Mills scales and the Planck mass MP. In contrast to SU(2)CMB [...] Read more.
Motivated by the SU(2)CMB modification of the cosmological model ΛCDM, we consider isolated fuzzy-dark-matter lumps, made of ultralight axion particles whose masses arise due to distinct SU(2) Yang–Mills scales and the Planck mass MP. In contrast to SU(2)CMB, these Yang–Mills theories are in confining phases (zero temperature) throughout most of the Universe’s history and associate with the three lepton flavours of the Standard Model of particle physics. As the Universe expands, axionic fuzzy dark matter comprises a three-component fluid which undergoes certain depercolation transitions when dark energy (a global axion condensate) is converted into dark matter. We extract the lightest axion mass ma,e=0.675×1023 eV from well motivated model fits to observed rotation curves in low-surface-brightness galaxies (SPARC catalogue). Since the virial mass of an isolated lump solely depends on MP and the associated Yang–Mills scale the properties of an e-lump predict those of μ- and τ-lumps. As a result, a typical e-lump virial mass ∼6.3×1010M suggests that massive compact objects in galactic centers such as Sagittarius A* in the Milky Way are (merged) μ- and τ-lumps. In addition, τ-lumps may constitute globular clusters. SU(2)CMB is always thermalised, and its axion condensate never has depercolated. If the axial anomaly indeed would link leptons with dark matter and the CMB with dark energy then this would demystify the dark Universe through a firmly established feature of particle physics. Full article
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11 pages, 2402 KiB  
Article
Influence of Fermions on Vortices in SU(2)-QCD
Universe 2021, 7(5), 130; https://doi.org/10.3390/universe7050130 - 04 May 2021
Cited by 3 | Viewed by 1258
Abstract
Gauge fields control the dynamics of fermions, and, in addition, a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the [...] Read more.
Gauge fields control the dynamics of fermions, and, in addition, a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also in the presence of fermionic fields. Full article
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14 pages, 3712 KiB  
Article
A Possible Resolution to Troubles of SU(2) Center Vortex Detection in Smooth Lattice Configurations
Universe 2021, 7(5), 122; https://doi.org/10.3390/universe7050122 - 29 Apr 2021
Cited by 4 | Viewed by 1228
Abstract
The center vortex model of quantum-chromodynamics can explain confinement and chiral symmetry breaking. We present a possible resolution for problems of the vortex detection in smooth configurations and discuss improvements for the detection of center vortices. Full article
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Review

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16 pages, 1144 KiB  
Review
Topological Aspects of Dense Matter: Lattice Studies
Universe 2021, 7(9), 336; https://doi.org/10.3390/universe7090336 - 09 Sep 2021
Cited by 1 | Viewed by 1340
Abstract
Topological fluctuations change their nature in the different phases of strong interactions, and the interrelation of topology, chiral symmetry and confinement at high temperature has been investigated in many lattice studies. This review is devoted to the much less explored subject of topology [...] Read more.
Topological fluctuations change their nature in the different phases of strong interactions, and the interrelation of topology, chiral symmetry and confinement at high temperature has been investigated in many lattice studies. This review is devoted to the much less explored subject of topology in dense matter. After a short overview of the status at zero density, which will serve as a baseline for the discussion, we will present lattice results for baryon rich matter, which, due to technical difficulties, has been mostly studied in two-color QCD, and for matter with isospin and chiral imbalances. In some cases, a coherent pattern emerges, and in particular the topological susceptibility seems suppressed at high temperature for baryon and isospin rich matter. However, at low temperatures the topological aspects of dense matter remain not completely clear and call for further studies. Full article
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55 pages, 5861 KiB  
Review
Different Faces of Confinement
Universe 2021, 7(9), 330; https://doi.org/10.3390/universe7090330 - 06 Sep 2021
Cited by 12 | Viewed by 1902
Abstract
In this review, we provide a short outlook of some of the current most popular pictures and promising approaches to non-perturbative physics and confinement in gauge theories. A qualitative and by no means exhaustive discussion presented here covers such key topics as the [...] Read more.
In this review, we provide a short outlook of some of the current most popular pictures and promising approaches to non-perturbative physics and confinement in gauge theories. A qualitative and by no means exhaustive discussion presented here covers such key topics as the phases of QCD matter, the order parameters for confinement, the central vortex and monopole pictures of the QCD vacuum structure, fundamental properties of the string tension, confinement realisations in gauge-Higgs and Yang–Mills theories, magnetic order/disorder phase transition, among others. Full article
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26 pages, 372 KiB  
Review
Confinement in 4D: An Attempt at Classical Understanding
Universe 2021, 7(8), 291; https://doi.org/10.3390/universe7080291 - 07 Aug 2021
Cited by 1 | Viewed by 1233
Abstract
In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. [...] Read more.
In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. We set out to ensure the presence of the massless photons—Goldstone bosons in Abelian theory and their disappearance in the Non-Abelian case—accompanied by the formation of confining strings between charged states. Our formulation avoids using vector fields and instead operates with the basic degrees of freedom that are the scalar fields of a nonlinear σ-model. The Mark 1 model we study turns out to have a large global symmetry group-the 2D diffeomorphism invariance in the Abelian limit, which is isomorphic to the group of all canonical transformations in the classical two dimensional phase space. This symmetry is not present in QED, and we eliminate it by “gauging” this infinite dimensional global group. Introducing additional modifications to the model (Mark 2), we are able to prove that the “Abelian” version is equivalent to the theory of a free photon. Achieving the desired property in the “Non-Abelian” regime turns out to be tricky. We are able to introduce a perturbation that leads to the formation of confining strings in our Mark 1 model. These strings have somewhat unusual properties, in that their profile does not decay exponentially away from the center of the string. In addition, the perturbation explicitly breaks the diffeomorphism invariance. Preserving this invariance in the gauged model as well as achieving confining strings in Mark 2 model remains an open question. Full article
23 pages, 775 KiB  
Review
From Center-Vortex Ensembles to the Confining Flux Tube
Universe 2021, 7(8), 253; https://doi.org/10.3390/universe7080253 - 21 Jul 2021
Cited by 6 | Viewed by 1855
Abstract
In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected [...] Read more.
In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension. Full article
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18 pages, 756 KiB  
Review
Superinsulators: An Emergent Realisation of Confinement
Universe 2021, 7(6), 201; https://doi.org/10.3390/universe7060201 - 17 Jun 2021
Cited by 1 | Viewed by 1684
Abstract
Superinsulators (SI) are a new topological state of matter, predicted by our collaboration and experimentally observed in the critical vicinity of the superconductor-insulator transition (SIT). SI are dual to superconductors and realise electric-magnetic (S)-duality. The effective field theory that describes this topological phase [...] Read more.
Superinsulators (SI) are a new topological state of matter, predicted by our collaboration and experimentally observed in the critical vicinity of the superconductor-insulator transition (SIT). SI are dual to superconductors and realise electric-magnetic (S)-duality. The effective field theory that describes this topological phase of matter is governed by a compact Chern-Simons in (2+1) dimensions and a compact BF term in (3+1) dimensions. While in a superconductor the condensate of Cooper pairs generates the Meissner effect, which constricts the magnetic field lines penetrating a type II superconductor into Abrikosov vortices, in superinsulators Cooper pairs are linearly bound by electric fields squeezed into strings (dual Meissner effect) by a monopole condensate. Magnetic monopoles, while elusive as elementary particles, exist in certain materials in the form of emergent quasiparticle excitations. We demonstrate that at low temperatures magnetic monopoles can form a quantum Bose condensate (plasma in (2+1) dimensions) dual to the charge condensate in superconductors. The monopole Bose condensate manifests as a superinsulating state with infinite resistance, dual to superconductivity. The monopole supercurrents result in the electric analogue of the Meissner effect and lead to linear confinement of the Cooper pairs by Polyakov electric strings in analogy to quarks in hadrons. Superinsulators realise thus one of the mechanism proposed to explain confinement in QCD. Moreover, the string mechanism of confinement implies asymptotic freedom at the IR fixed point. We predict thus for superinsulators a metallic-like low temperature behaviour when samples are smaller than the string scale. This has been experimentally confirmed. We predict that an oblique version of SI is realised as the pseudogap state of high-TC superconductors. Full article
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43 pages, 1154 KiB  
Review
Localization of Dirac Fermions in Finite-Temperature Gauge Theory
Universe 2021, 7(6), 194; https://doi.org/10.3390/universe7060194 - 08 Jun 2021
Cited by 14 | Viewed by 1899
Abstract
It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. [...] Read more.
It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models. Full article
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28 pages, 454 KiB  
Review
Effective String Description of the Confining Flux Tube at Finite Temperature
Universe 2021, 7(6), 170; https://doi.org/10.3390/universe7060170 - 30 May 2021
Cited by 12 | Viewed by 1778
Abstract
In this review, after a general introduction to the Effective String Theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several [...] Read more.
In this review, after a general introduction to the Effective String Theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement. Full article
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