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Journal articles on the topic 'Quantum chromodynamics; Abelian projection'
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1
Shinohara, Toru. "Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics II." Modern Physics Letters A 18, no. 20 (June 28, 2003): 1403–12. http://dx.doi.org/10.1142/s0217732303011198.
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In the previous paper,1 we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU (N) Yang–Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian antisymmetric tensor field. In this paper, we show the multiplicative renormalizability of the Green's functions also for the off-diagonal gluon. Moreover, we complement the previous results by calculating the anomalous dimension and the renormalization group functions which are undetermined in the previous paper.
2
Kondo, K. I., and T. Shinohara. "Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics." Progress of Theoretical Physics 105, no. 4 (April 1, 2001): 649–65. http://dx.doi.org/10.1143/ptp.105.649.
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Nishijima, K. "Renormalization Group and Color Confinement." International Journal of Modern Physics B 12, no. 12n13 (May 30, 1998): 1355–64. http://dx.doi.org/10.1142/s0217979298000764.
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Aste, Andreas. "Comment on "A simple explanation of the nonappearance of physical gluons and quarks"." Canadian Journal of Physics 81, no. 6 (June 1, 2003): 889–91. http://dx.doi.org/10.1139/p03-056.
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In a recent paper by Johan Hansson it is claimed that the nonappearance of quarks and gluons as physical particles is an automatic result of the non-Abelian nature of the color interaction in quantum chromodynamics. It is shown that the arguments given by Hansson are insufficient to support his claim by giving simple counter arguments. PACS No.: 11.10.z
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Creutz, Michael. "QCD beyond diagrams." International Journal of Modern Physics A 36, no. 21 (July 30, 2021): 2130012. http://dx.doi.org/10.1142/s0217751x2130012x.
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Quantum chromodynamics (QCD), the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation and chiral symmetry breaking. This paper is a colloquium level overview of the framework for understanding how these effects come about.
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Rana, J. M. S., H. C. Chandola, and B. S. Rajput. "The quark confinement in extended gauge theory." Canadian Journal of Physics 69, no. 12 (December 1, 1991): 1441–46. http://dx.doi.org/10.1139/p91-213.
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To investigate the possible physical implications of the topological structure of non-Abelian dyons in connection with the issue of quark confinement in quantum chromodynamics (QCD), extended gauge theory is formulated in SU(2) and SU(3) gauge groups from the corresponding restricted chromodynamics (RCD) by reactivating the suppressed dynamical degrees of freedom and constructing the gauge potential in terms of the binding gluons (the RCD piece) and the valence gluons (the reactivated piece). It is shown that in this extended QCD, the confinement mechanism of the corresponding RCD remains intact. The physical spectrum contains color-singlet generalized electric glueballs made of valence gluon pairs as well as the generalized magnetic glueballs as massive collective modes of the condensed vacuum.
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Tainov, V. A. "DOMAIN WALL NETWORK AS QCD VACUUM: CORRELATION FUNCTIONS AND CONFINEMENT OF STATIC QUARKS." Bulletin of Dubna International University for Nature, Society, and Man. Series: Natural and engineering sciences, no. 4 (45) (December 30, 2019): 38–47. http://dx.doi.org/10.37005/1818-0744-2019-4-38-47.
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Within the domain model of QCD vacuum the properties of a statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields representing the physical vacuum of quantum chromodynamics are investigated. The two-point correlation function of the topological charge density is calculated and the topological susceptibility is found. It is shown that such vacuum fields ensure the implementation of the area law for the Wilson loop, i.e. the confinement of static quarks.
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Yang, Weihua. "Parity-odd parton distribution functions from 𝜃-vacuum." International Journal of Modern Physics A 34, no. 26 (September 20, 2019): 1950145. http://dx.doi.org/10.1142/s0217751x19501458.
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Quantum chromodynamics is a fundamental non-Abelian gauge theory of strong interactions. The physical quantum chromodynamics vacuum state is a linear superposition of the [Formula: see text]-vacua states with different topological numbers. Because of the configuration of the gauge fields, the tunneling events can induce the local parity-odd domains. Those interactions that occur in these domains can be affected by these effects. Considering the hadron (nucleon) system, we introduce the parity-odd parton distribution functions in order to describe the parity-odd structures inside the hadron in this paper. We obtain 8 parity-odd parton distribution functions at leading twist for spin-1/2 hadrons and present their properties. By introducing the parity-odd quark–quark correlator, we find the parity-odd effects vanish from the macroscopic point of view. In this paper, we consider the high energy semi-inclusive deeply inelastic scattering process to investigate parity-odd effects by calculating the spin asymmetries.
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Suganuma, Hideo, and Hiroki Ohata. "Local Correlation among the Chiral Condensate, Monopoles, and Color Magnetic Fields in Abelian Projected QCD." Universe 7, no. 9 (August 28, 2021): 318. http://dx.doi.org/10.3390/universe7090318.
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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 r≃0.8 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.
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Deguchi, Shinichi, and Yousuke Kokubo. "Abelian Projection of Massive SU(2) Yang–Mills Theory." Modern Physics Letters A 18, no. 29 (September 21, 2003): 2051–70. http://dx.doi.org/10.1142/s0217732303011952.
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We derive an effective Abelian gauge theory (EAGT) of a modified SU(2) Yang–Mills theory. The modification is made by explicitly introducing mass terms of the off-diagonal gluon fields into pure SU(2) Yang–Mills theory, in order that Abelian dominance at a long-distance scale is realized in the modified theory. In deriving the EAGT, the off-diagonal gluon fields involving longitudinal modes are treated as fields that produce quantum effects on the diagonal gluon field and other fields relevant at a long-distance scale. Unlike earlier papers, a necessary gauge fixing is carried out without spoiling the global SU(2) gauge symmetry. We show that the EAGT allows a composite of the Yukawa and the linear potentials which also occurs in an extended dual Abelian Higgs model. This composite potential is understood to be a static potential between color-electric charges. In addition, we point out that the EAGT involves the Skyrme–Faddeev model.
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Vizgin, Vladimir P. "“Comedy of mistakes” and “drama of humans”: on the domestic contribution to the creation of The Standard Model of elemantary particle in physics." Science management: theory and practice 2, no. 3 (2020): 196–224. http://dx.doi.org/10.19181/smtp.2020.2.3.11.
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The article explores domestic contribution to the creation of The Standard Model (SM). SM is a quantum field gauge theory of electromagnetic, weak and strong interactions, which is the basis of the modern theory of elementary particles. The process of its development covers a twenty-year period – from 1954 (the concept of non-Abelian Yang-Mills gauge fields) to the early 1970s, when the construction of renormalizable quantum chromodynamics and electroweak theory was completed. The reasons for the difficult perception of the Yang-Mills gauge field concept in the USSR are analyzed, associated primarily with the problem of “zero-charge” in quantum electrodynamics, and then in field theories of strong and weak interactions. This result, obtained by the leaders of the outstanding Russian scientific schools of theoretical physics, L. D. Landau, I. Ya. Pomeranchuk and their students, led to the rejection of the majority of Soviet physicists from field theory and to their transition to the position of a non-field phenomenological program (based on the S-matrix theory) in the construction of the theory of elementary particles.
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Balachandran, A. P. "QCD breaks Lorentz invariance and colour." Modern Physics Letters A 31, no. 10 (March 28, 2016): 1650060. http://dx.doi.org/10.1142/s0217732316500607.
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In the previous work [A. P. Balachandran and S. Vaidya, Eur. Phys. J. Plus 128, 118 (2013)], we have argued that the algebra of non-Abelian superselection rules is spontaneously broken to its maximal Abelian subalgebra, that is, the algebra generated by its completing commuting set (the two Casimirs, isospin and a basis of its Cartan subalgebra). In this paper, alternative arguments confirming these results are presented. In addition, Lorentz invariance is shown to be broken in quantum chromodynamics (QCD), just as it is in quantum electrodynamics (QED). The experimental consequences of these results include fuzzy mass and spin shells of coloured particles like quarks, and decay life times which depend on the frame of observation [D. Buchholz, Phys. Lett. B 174, 331 (1986); D. Buchholz and K. Fredenhagen, Commun. Math. Phys. 84, 1 (1982; J. Fröhlich, G. Morchio and F. Strocchi, Phys. Lett. B 89, 61 (1979); A. P. Balachandran, S. Kürkçüoğlu, A. R. de Queiroz and S. Vaidya, Eur. Phys. J. C 75, 89 (2015); A. P. Balachandran, S. Kürkçüoğlu and A. R. de Queiroz, Mod. Phys. Lett. A 28, 1350028 (2013)]. In a paper under preparation, these results are extended to the ADM Poincaré group and the local Lorentz group of frames. The renormalisation of the ADM energy by infrared gravitons is also studied and estimated.
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Yang, Weihua, and Fei Huang. "Deep inelastic scattering in the target fragmentation region." International Journal of Modern Physics A 35, no. 32 (November 20, 2020): 2050212. http://dx.doi.org/10.1142/s0217751x20502127.
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Deep inelastic scattering is one of the best place to study hadron structures. In this paper we consider the target fragmentation region deep inelastic scattering process at leading twist. The calculations are carried out by applying the collinear expansion. In the collinear expansion formalism the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. Quantum chromodynamics is a non-Abelian gauge theory of strong interactions in which parity symmetry can be violated by the nontrivial [Formula: see text]-vacuum tunneling effects. As a result, the axial vector current is induced. By defining and decomposing the parity-odd correlator we calculate both the parity-even and parity-odd contributions to the cross-section of the target fragmentation region deep inelastic scattering. We also present the positivity bounds for these fracture functions.
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Bignell, Ryan, Waseem Kamleh, and Derek Leinweber. "Computing the magnetic field response of the proton." EPJ Web of Conferences 245 (2020): 06033. http://dx.doi.org/10.1051/epjconf/202024506033.
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Background field methods offer an approach through which fundamental non-perturbative hadronic properties can be studied. Lattice QCD is the only ab initio method with which Quantum Chromodynamics can be studied at low energies; it involves numerically calculating expectation values in the path integral formalism. This requires substantial investment in high performance supercomputing resources. A particular challenge of lattice QCD is isolating the desired state, rather than a superposition of excited states. While extensive work has been performed which allows the ground state to be identified in lattice QCD calculations, this remains a challenging proposition for the ground state in the presence of a uniform magnetic field field. Quark level projection operators are introduced to resolve this challenge and thus allow for extraction of the magnetic polarisability.
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Yang, Weihua. "Parity-odd fragmentation functions." International Journal of Modern Physics A 34, no. 25 (September 9, 2019): 1950144. http://dx.doi.org/10.1142/s0217751x19501446.
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Quantum chromodynamics is a non-Abelian gauge theory of strong interactions, in which the parity symmetry can be violated by the nontrivial [Formula: see text]-vacuum tunneling effects. The [Formula: see text]-vacuum induces the local parity-odd domains. Those reactions that occur in these domains can be affected by the tunneling effects and quantities become parity-odd. In this paper we consider the fragmentation process where parity-odd fragmentation functions are introduced. We present the fragmentation functions by decomposing the quark–quark correlator. Among the total 16 fragmentation functions, eight of them are parity conserved, and the others are parity violated. They have a one-to-one correspondence. Positivity bounds of these one-dimensional fragmentation functions are shown. To be explicit, we also introduce an operator definition of the parity-odd correlator. According to the definition, we give a proof that the parity-odd fragmentation functions are local quantities and vanish when sum over all the hadrons [Formula: see text].
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Dzhunushaliev, Vladimir, Vladimir Folomeev, Tlekkabul Ramazanov, and Tolegen Kozhamkulov. "Thermodynamics and statistical physics of quasiparticles within the quark–gluon plasma model." Modern Physics Letters A 35, no. 23 (June 16, 2020): 2050194. http://dx.doi.org/10.1142/s0217732320501941.
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We consider thermodynamic properties of a quark–gluon plasma related to quasiparticles having the internal structure. For this purpose, we employ a possible analogy between quantum chromodynamics and non-Abelian Proca-Dirac-Higgs theory. The influence of characteristic sizes of the quasiparticles on such thermodynamic properties of the quark–gluon plasma like the internal energy and pressure is studied. Sizes of the quasiparticles are taken into account in the spirit of the van der Waals equation but we take into consideration that the quasiparticles have different sizes, and the average value of these sizes depends on temperature. It is shown that this results in a change in the internal energy and pressure of the quark–gluon plasma. Also, we show that, when the temperature increases, the average value of characteristic sizes of the quasiparticles increases as well. This leads to the occurrence of a phase transition at the temperature at which the volume occupied by the quasiparticles is compared with the volume occupied by the plasma.
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Lee, Bum-Hoon, Youngman Kim, D. G. Pak, Takuya Tsukioka, and P. M. Zhang. "Gauge invariant gluon spin operator for spinless nonlinear wave solutions." International Journal of Modern Physics A 32, no. 11 (April 13, 2017): 1750062. http://dx.doi.org/10.1142/s0217751x17500622.
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We consider nonlinear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU(2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of static Wu–Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which is supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.
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Giordano, Matteo, and Tamás Kovács. "Localization of Dirac Fermions in Finite-Temperature Gauge Theory." Universe 7, no. 6 (June 8, 2021): 194. http://dx.doi.org/10.3390/universe7060194.
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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.
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ANDRIANOV, A. A., D. ESPRIU, and A. PRATS. "CHIRAL DYNAMICS FROM THE HADRONIC STRING: GENERAL FORMALISM." International Journal of Modern Physics A 21, no. 16 (June 30, 2006): 3337–65. http://dx.doi.org/10.1142/s0217751x06031314.
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Quantum Chromodynamics (QCD) at long distances can be described by the chiral Lagrangian. On the other hand there is overwhelming evidence that QCD and all non-Abelian theories admit an effective string description. Here we review a derivation of the (intrinsic) parity-even chiral Lagrangian by requiring that the propagation of the QCD string takes place on a background where chiral symmetry is spontaneously broken. Requiring conformal invariance leads to the equation of motion of the chiral Lagrangian. We then proceed to coupling the string degrees of freedom to external gauge fields and we recover in this way the covariant equations of motion of the gauge-invariant chiral Lagrangian at [Formula: see text]. We consider next the parity-odd part (Wess–Zumino–Witten) action and argue that this requires the introduction of the spin degrees of freedom (absent in the usual effective action treatment). We manage to reproduce the Wess–Zumino–Witten term in two dimensions (2D) in an unambiguous way. In 4D the situation is considerably more involved. We outline the modification of boundary interaction that is necessary to induce the parity-odd part of the chiral Lagrangian.
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Morreale, Astrid, and Farid Salazar. "Mining for Gluon Saturation at Colliders." Universe 7, no. 8 (August 23, 2021): 312. http://dx.doi.org/10.3390/universe7080312.
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Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains.
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DAS, C. R., L. V. LAPERASHVILI, and H. B. NIELSEN. "GENERALIZED DUAL SYMMETRY OF NON-ABELIAN THEORIES AND THE FREEZING OF αs." International Journal of Modern Physics A 21, no. 22 (September 10, 2006): 4479–510. http://dx.doi.org/10.1142/s0217751x06033246.
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The quantum Yang–Mills theory, describing a system of fields with nondual (chromoelectric g) and dual (chromomagnetic [Formula: see text]) charges and revealing the generalized dual symmetry, is developed by analogy with the Zwanziger formalism in QED. The renormalization group equations (RGE's) for pure non-Abelian theories are analyzed for both constants, α = g2/4π and [Formula: see text]. The pure [Formula: see text] gauge theory is investigated as an example. We consider not only monopoles, but also dyons. The behavior of the total SU(3) β-function is investigated in the whole region of α≡αs: 0≤α < ∞. It is shown that this β-function is antisymmetric under the interchange α ↔ 1/α and is given by the well-known perturbative expansion not only for α≪1, but also for α≫1. Using an idea of the Maximal Abelian Projection by 't Hooft, we have considered the formation of strings — the ANO flux tubes — in the Higgs model of scalar monopole (or dyon) fields. In this model we have constructed the behavior of the β-function in the vicinity of the point α = 1, where it acquires a zero value. Considering the phase transition points at α≈0.4 and α≈2.5, we give the explanation of the freezing of αs. The evolution of [Formula: see text] with energy scale μ and the behavior of V eff (μ) are investigated for both, perturbative and nonperturbative regions of QCD. It was shown that the effective potential has a minimum, ensured by the dual sector of QCD. The gluon condensate [Formula: see text], corresponding to this minimum, is predicted: [Formula: see text], in agreement with the well-known results.
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GABADADZE, GREGORY, and ZURAB KAKUSHADZE. "ZERO-BRANE MATRIX MECHANICS, MONOPOLES AND MEMBRANE APPROACH IN QCD." Modern Physics Letters A 15, no. 04 (February 10, 2000): 293–308. http://dx.doi.org/10.1142/s0217732300000281.
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We conjecture that a T-dual form of pure QCD describes dynamics of point-like monopoles. T-duality transforms the QCD Lagrangian into a matrix quantum mechanics of zero-branes which we identify with monopoles. At generic points of the monopole moduli space, the SU (N) gauge group is broken down to U (1)N-1 reproducing the key feature of 't Hooft's Abelian projection. There are certain points in the moduli space where monopole positions coincide, gauge symmetry is enhanced and gluons emerge as massless excitations. We show that there is a linearly rising potential between zero-branes. This indicates the presence of a stretched flux tube between monopoles. The lowest energy state is achieved when monopoles are sitting on top of each other and gauge symmetry is enhanced. In this case they behave as free massive particles and can be condensed. In fact, we find a constant eigenfunction of the corresponding Hamiltonian which describes condensation of monopoles. Using the monopole quantum mechanics, we argue that large-N QCD in this T-dual picture is a theory of a closed bosonic membrane propagating in five-dimensional space–time. QCD point-like monopoles can be regarded in this approach as constituents of the membrane.
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Ladrem, Madjid Lakhdar Hamou, Mohammed Abdulmalek Abdulraheem Ahmed, Salah Cherif, Zainab Zaki Mohammed Alfull, and Mosleh M. Almarashi. "Detailed study of the QCD Equation of State of a colorless partonic plasma in finite volume." International Journal of Modern Physics A 34, no. 09 (March 30, 2019): 1950051. http://dx.doi.org/10.1142/s0217751x19500519.
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The color confinement in Quantum Chromodynamics (QCD) remains an interesting and intriguing phenomenon. It is considered as a very important nonperturbative effect to be taken into account in all models intended to describe the QCD many-parton system. During the deconfinement phase transition, the non-Abelian character of the partonic plasma manifests itself in an important manner. A direct consequence of color confinement is that all states of any partonic system must be colorless and the requirement of the colorlessness condition is more than necessary. Indeed, the colorless state is a result of the multiparton interactions, from which collective phenomena can emerge, inducing strong correlations and giving rise to a long-range order of liquid-like phase, a behavior fundamentally different from that of a conformal ideal gas. Within our Colorless QCD MIT-Bag Model and using the [Formula: see text]-method, three Thermal Response Functions, related to the Equation of State, like pressure [Formula: see text], sound velocity [Formula: see text] and energy density [Formula: see text] are calculated and studied as functions of temperature [Formula: see text] and volume [Formula: see text]. Also and in the same context, two relevant correlation forms [Formula: see text] and [Formula: see text] are calculated and studied intensively as functions of [Formula: see text] at different volumes. A detailed comparative study between our results and those obtained from lattice QCD simulation, hot QCD and other phenomenological models is carried out. We find that the Liquid Partonic Plasma Model is the model which fits our Equation of State very well, in which the Bag constant term is revealed very important. Our Colorless Partonic Plasma, just beyond the finite volume transition point, is found in a state where the different partons interact strongly showing a liquid behavior in agreement with the estimate of the plasma parameter [Formula: see text] and supporting the result obtained from the fitting work. This allows us to understand experimental observations in Ultra-Relativistic Heavy-Ion Collisions and to interpret lattice QCD results.
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BESANA, ALBERTO, and MAURO SPERA. "ON SOME SYMPLECTIC ASPECTS OF KNOT FRAMINGS." Journal of Knot Theory and Its Ramifications 15, no. 07 (September 2006): 883–912. http://dx.doi.org/10.1142/s0218216506004798.
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The present article delves into some symplectic features arising in basic knot theory. An interpretation of the writhing number of a knot (with reference to a plane projection thereof) is provided in terms of a phase function analogous to those encountered in geometrical optics, its variation upon switching a crossing being akin to the passage through a caustic, yielding a knot theoretical analogue of Maslov's theory, via classical fluidodynamical helicity. The Maslov cycle is given by knots having exactly one double point, among those having a fixed plane shadow and lying on a semi-cone issued therefrom, which turn out to build up a Lagrangian submanifold of Brylinski's symplectic manifold of (mildly) singular knots. A Morse family (generating function) for this submanifold is determined and can be taken to be the Abelian Chern–Simons action plus a source term (knot insertion) appearing in the Jones–Witten theory. The relevance of the Bohr–Sommerfeld conditions arising in geometric quantization are investigated and a relationship with the Gauss linking number integral formula is also established, together with a novel derivation of the so-called Feynman–Onsager quantization condition. Furthermore, an additional Chern–Simons interpretation of the writhe of a braid is discussed and interpreted symplectically, also making contact with the Goldin–Menikoff–Sharp approach to vortices and anyons. Finally, a geometrical setting for the ground state wave functions arising in the theory of the Fractional Quantum Hall Effect is established.
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Gorsky, A., M. Shifman, and A. Yung. "N=1supersymmetric quantum chromodynamics: How confined non-Abelian monopoles emerge from quark condensation." Physical Review D 75, no. 6 (March 30, 2007). http://dx.doi.org/10.1103/physrevd.75.065032.
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Cherchiglia, A., D. C. Arias-Perdomo, A. R. Vieira, M. Sampaio, and B. Hiller. "Two-loop renormalisation of gauge theories in 4D implicit regularisation and connections to dimensional methods." European Physical Journal C 81, no. 5 (May 2021). http://dx.doi.org/10.1140/epjc/s10052-021-09259-6.
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AbstractWe compute the two-loop $$\beta $$ β -function of scalar and spinorial quantum electrodynamics as well as pure Yang–Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using implicit regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.
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Eto, Minoru, Yuji Hirono, Muneto Nitta, and Shigehiro Yasui. "Vortices and other topological solitons in dense quark matter." Progress of Theoretical and Experimental Physics 2014, no. 1 (January 1, 2014). http://dx.doi.org/10.1093/ptep/ptt095.
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Abstract Dense quantum chromodynamic matter accommodates various kind of topological solitons such as vortices, domain walls, monopoles, kinks, boojums, and so on. In this review, we discuss various properties of topological solitons in dense quantum chromodynamics (QCD) and their phenomenological implications. Particular emphasis is placed on the topological solitons in the color–flavor-locked (CFL) phase, which exhibits both superfluidity and superconductivity. The properties of topological solitons are discussed in terms of effective field theories such as the Ginzburg–Landau theory, the chiral Lagrangian, or the Bogoliubov–de Gennes equation. The most fundamental string-like topological excitations in the CFL phase are non-Abelian vortices, which are 1/3 quantized superfluid vortices and color magnetic flux tubes. These vortices are created at a phase transition by the Kibble–Zurek mechanism or when the CFL phase is realized in compact stars, which rotate rapidly. The interaction between vortices is found to be repulsive and consequently a vortex lattice is formed in rotating CFL matter. Bosonic and fermionic zero-energy modes are trapped in the core of a non-Abelian vortex and propagate along it as gapless excitations. The former consists of translational zero modes (a Kelvin mode) with a quadratic dispersion and ${\mathbb {C}}P^2$ Nambu–Goldstone gapless modes with a linear dispersion, associated with the CFL symmetry spontaneously broken in the core of a vortex, while the latter is Majorana fermion zero modes belonging to the triplet of the symmetry remaining in the core of a vortex. The low-energy effective theory of the bosonic zero modes is constructed as a non-relativistic free complex scalar field and a relativistic ${\mathbb {C}}P^2$ model in 1+1 dimensions. The effects of strange quark mass, electromagnetic interactions, and non-perturbative quantum corrections are taken into account in the ${\mathbb {C}}P^2$ effective theory. Various topological objects associated with non-Abelian vortices are studied; colorful boojums at the CFL interface, the quantum color magnetic monopole confined by vortices, which supports the notion of quark–hadron duality, and Yang–Mills instantons inside a non-Abelian vortex as lumps are discussed. The interactions between a non-Abelian vortex and quasiparticles such as phonons, gluons, mesons, and photons are studied. As a consequence of the interaction with photons, a vortex lattice behaves as a cosmic polarizer. As a remarkable consequence of Majorana fermion zero modes, non-Abelian vortices are shown to behave as a novel kind of non-Abelian anyon. In the order parameters of chiral symmetry breaking, we discuss fractional and integer axial domain walls, Abelian and non-Abelian axial vortices, axial wall–vortex composites, and Skyrmions.
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Ravasio, Silvia Ferrario, Giovanni Limatola, and Paolo Nason. "Infrared renormalons in kinematic distributions for hadron collider processes." Journal of High Energy Physics 2021, no. 6 (June 2021). http://dx.doi.org/10.1007/jhep06(2021)018.
Full textAbstract:
Abstract Infrared renormalons in Quantum Chromodynamics are associated with non-perturbative corrections to short distance observables. Linear renormalons, i.e. such that the associated non-perturbative corrections scale like one inverse power of the hard scale, can affect at a non-negligible level even the very high-energy phenomena studied at the Large Hadron Collider. Using an Abelian model, we study the presence of linear renormalons in the transverse momentum distribution of a neutral vector boson Z produced in hadronic collisions. We consider a process where the Z transverse momentum is balanced by a sizable recoil against a coloured final state particle. One may worry that such a colour configuration, not being azimuthally symmetric, could generate unbalanced soft radiation, associated in turn with linear infrared renormalons affecting the transverse momentum distribution of the vector boson. We performed a numerical calculation of the renormalon effects for this process in the so-called large b0 limit. We found no evidence of linear renormalons in the transverse momentum distribution of the Z in the large transverse-momentum region, irrespective of rapidity cuts.