Monopoles In QCD Research Articles

Searching for GUT-scale QCD axions and monopoles with a high-voltage capacitor

Searching for GUT-scale QCD axions and monopoles with a high-voltage capacitor

An Effective Model for Glueballs and Dual Superconductivity at Finite Temperature

The glueballs lead to gluon and QCD monopole condensations as by-products of color confinement. A color dielectric function G ∣ ϕ ∣ coupled with a Abelian gauge field is properly defined to mediate the glueball interactions at confining regime after spontaneous symmetry breaking (SSB) of the gauge symmetry. The particles are expected to form through the quark-gluon plasma (QGP) hadronization phase where the free quarks and gluons start clamping together to form hadrons. The QCD-like vacuum η 2 m η 2 F μ ν F μ ν , confining potential V c r , string tension σ , penetration depth λ , superconducting and normal monopole densities ( n s n n ), and the effective masses ( m η 2 and m A 2 ) will be investigated at finite temperature T . We also calculate the strong “running” coupling α s and subsequently the QCD β -function. The dual superconducting nature of the QCD vacuum will be investigated based on monopole condensation.

Confinement of Fermions in Tachyon Matter

In this paper, we develop a phenomenological model inspired by QCD that mimics the QCD theory. We use the gauge theory in color dielectric medium (Gϕ) coupled with fermion fields to produce scalar and vector confinements in the chromoelectric flux tube scenario. The Abelian theory will be used to approximate the non-Abelian QCD theory in a consistent manner. We will calculate vector and scalar glueballs and compare the result to the existing simulation and experimental results and projections. The QCD-like vacuum associated with the model will be calculated and its behavior studied relative to changing quark masses. We will also comment on the relationship between tachyon condensation, dual Higgs mechanism, QCD monopole condensation, and their association with confinement. The behavior of the QCD string tension obtained from the vector potential of the model will be studied to establish vector dominance in confinement theories.

Chiral symmetry breaking and monopoles in gauge theories

QCD monopoles are magnetically charged quasiparticles whose Bose-Einstein condensation (BEC) at $T<T_c$ creates electric confinement and flux tubes. The "magnetic scenario" of QCD proposes that scattering on the non-condensed component of the monopole ensemble at $T>T_c$ plays an important role in explaining the properties of strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. In this paper, we study the phenomenon of chiral symmetry breaking and its relation to magnetic monopoles. Specifically, we study the eigenvalue spectrum of the Dirac operator in the basis of fermionic zero modes in an SU(2) monopole background. We find that as the temperature approaches the deconfinement temperature $T_c$ from above, the eigenvalue spectrum has a finite density at $\omega = 0$, indicating the presence of a chiral condensate. In addition, we find the critical scaling of the eigenvalue gap to be consistent with that of the correlation length in the 3d Ising model and the BEC transition of monopoles on the lattice.

Role of QCD monopoles in jet quenching

QCD monopoles are magnetically charged quasiparticles whose Bose-Einstein condensation (BEC) at $T<T_c$ creates electric confinement and flux tubes. The "magnetic scenario" of QCD proposes that scattering on the non-condensed component of the monopole ensemble at $T>T_c$ is responsible for the unusual kinetic properties of QGP. In this paper, we study the contribution of the monopoles to jet quenching phenomenon, using the BDMPS framework and hydrodynamic backgrounds. In the lowest order for cross sections, we calculate the nuclear modification factor, $R_\text{AA},$ and azimuthal anisotropy, $v_2$, of jets, as well as the dijet asymmetry, $A_j$, and compare those to the available data. We find relatively good agreement with experiment when using realistic hydrodynamic backgrounds. In addition, we find that event-by-event fluctuations are not necessary to reproduce $R_\text{AA}$ and $v_2$ data, but play a role in $A_j$. Since the monopole-induced effects are maximal at $T\approx T_c$, we predict that their role should be significantly larger, relative to quarks and gluons, at lower RHIC energies.

An Effective Model of QCD Monopoles

In this work, we carried out quantum many-body studies of magnetic monopole ensembles through numerical simulations of the path integral for one- and two-component Coulomb Bose systems. We found the relation between the critical temperature for the Bose-Einstein condensation phase transition and the Coulomb coupling strength using two methods, the finite-size scaling of the superfluid fraction and statistical analysis of permutation cycles. After finding parameters that match the correlation functions measured in our system with the correlation functions previously measured on the lattice, we arrived at an effective quantum model of color magnetic monopoles in QCD. From this matched model, we were able to extract the monopole contribution to QCD equation of state near Tc. This proceeding and the given talk are based on [A. Ramamurti and E. Shuryak, Phys. Rev. D 95, 076019 (2017). doi:10.1103/PhysRevD.95.076019].

Chiral symmetry breaking by monopole condensation

Under the assumption of Abelian dominance in QCD, we have shown that chiral condensate is locally present around each QCD monopole. The essence is that either charge or chirality of a quark is not conserved, when the low energy massless quark collides with QCD monopole. In reality, the charge is conserved so that the chirality is not conserved. Reviewing the presence of the local chiral condensate, we show by using chiral anomaly that chiral nonsymmetric quark pair production takes place when a color charge is putted in a vacuum with monopole condensation, while chiral symmetric pair production takes place in a vacuum with no monopole condensation. Our results strongly indicate that the chiral symmetry is broken by the monopole condensation.

QCD monopole and sigma meson coupling

Under the assumption of the Abelian dominance in QCD, we show that chiral condensate is locally present around a QCD monopole. The appearance of the chiral condensate around a GUT monopole was shown in the previous analysis of the Rubakov effect. We apply a similar analysis to the QCD monopole. It follows that the condensation of the monopole carrying the chiral condensate leads to the chiral symmetry breaking as well as quark confinement. To realize the result explicitly, we present a phenomenological linear sigma model coupled with the monopoles, in which the monopole condensation causes the chiral symmetry breaking as well as confinement. The monopoles are assumed to be described by a model of dual superconductor. Because the monopoles couple with mesons, we point out the presence of an observable color singlet monopole coupled with the mesons.

Monopoles and the Polyakov loop

We propose a new order parameter of a $Z_N$ symmetry in SU(N) gauge theories in $4$ dimensional Minkowski space-time, assuming spatial periodic boundary conditions. It is given by $Tr(P\exp(i\int_c A_{\mu}dx^{\mu}))$ where the spatial path $c$ is taken, for example, along $x_1$ axis. The parameter vanishes when the $Z_N$ symmetry is preserved. We calculate the contribution of QCD monopoles to the order parameter and show that when the monopoles condense $\langle\Phi\rangle\neq 0$, it vanishes, while it does not vanish when they do not condense. These calculations are performed using a monopole field $\Phi$ canonically quantized in a model of dual superconductor.

Effective model of QCD magnetic monopoles from numerical study of one- and two-component Coulomb quantum Bose gases

Magnetic monopoles are suggested to play an important role in strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. So far, their many-body treatment has only been done classically, with just binary scattering solved in quantum mechanics. In this paper we start quantum many-body studies of the monopole ensembles. Specifically, we carry out numerical simulations of the path integral for one- and two-component Coulomb Bose systems. We determine the relation between the critical temperature for the Bose-Einstein condensation phase transition $T_\text{c}$ and the Coulomb coupling strength using two methods, the classic finite-size scaling of the condensate and a lattice-tested method based on permutation cycles. For a one-component Coulomb Bose gas, we observe the same behavior of the critical temperature -- initially rising slightly then falling as interaction strength is increased -- as seen in the case of hard spheres; we also observe the same behavior for a two-component Coulomb Bose gas. We then calculate sets of radial correlation functions between the like and unlike charged particles. By matching those with the correlation functions previously calculated on the lattice, we derive an effective quantum model of color magnetic monopoles in QCD. From this matched model, we are able to extract the monopole contribution to QCD equation of state near $T_\text{c}$.

Dual QCD, confinement potential and thermal effects

Based on the topological structure of non-Abelian gauge theories, a dual QCD gauge formulation has been developed in terms of magnetic symmetry, which manifests the topological structure of the symmetry group in a non-trivial way. The dynamical configuration of the resulting dual QCD vacuum and its flux tube configuration have been investigated for analyzing the non-perturbative features of QCD. Utilizing the dual QCD Lagrangian in the dynamically broken phase of magnetic symmetry and applying Zwanziger formalism, the non-perturbative gluon propagator has been derived and used to extract the quark confining potential for both quenched and full QCD. The quenched confining mechanism is responsible for linear confinement and points towards the permanent confinement of the colored quarks inside the hadrons. In full QCD due to light-quark polarization the quark-antiquark potential automatically screens signaling the instability in the flux tube at large inter-quark distances and such screening increases with the increase of infrared cutoff. Using the partition function approach alongwith the mean-field treatment for the QCD monopole field the thermal response of the QCD vacuum has been analyzed by deriving the finite-temperature form of quark confining potential. A continuous vanishing of the associated string tension has been observed in the vicinity of critical temperature, which, in turn, leads to the restoration of magnetic symmetry in the domain of high temperatures and signals the onset of second-order deconfinement phase transition.

About monopoles in QCD

The hypothesis is analysed that the monopoles condensing in QCD vacuum to make it a dual superconductor are classical solutions of the equations of motion.

QCD Monopoles on the Lattice and Gauge Invariance

The long standing problem is solved why the number and the location of monopoles observed in Lattice configurations depend on the choice of the gauge used to detect them, in contrast to the obvious requirement that monopoles, as physical objects, must have a gauge-invariant status. It is proved, by use of non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and controllable way.

Magnetic Symmetry, Regge Trajectories and the Linear Confinement in Dual QCD

Using the magnetic symmetry structure of non-Abelian gauge theories, we analyze the flux tube formulation and its implications on the hadronic Regge trajectories and the confinement of color isocharges in magnetically condensed (with as well as without the electric excitations) QCD vacuum. Starting with the fiber bundle structure of QCD, the dual potentials are used to construct the QCD Lagrangian which has been shown to develop a unique flux tube configuration in its dynamically broken phase. The vector mass mode of the condensed vacuum has been shown to play a leading role in flux tube energy and other confinement parameters. Using the flux tube energy and the angular momentum, the Regge trajectories for hadrons have been obtained and the linear confining properties of dual QCD have been established. The dyonic flux tube structure of the condensed QCD vacuum has been obtained by inducing the electric excitation of QCD monopoles and the confining nature along with the linearity of Regge trajectories in dyonically condensed QCD vacuum are shown to remain intact. Implications of the modification in Regge slope parameter, on improving the confining properties of dual QCD vacuum are also discussed.

Analytic estimate of the order parameter for monopole condensation in QCD

The disorder parameter for the condensation of monopoles in QCD is estimated analytically in terms of gauge invariant field-strength correlators. The continuum limit is discussed.

Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills theory

We study the embedded QCD monopoles (``quark monopoles'') using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial, and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anticorrelated with the density of the Dirac eigenmodes. We observe that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low-temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the stringlike objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core which is, however, empty at the very center of the monopole.

Kertész Line and Embedded Monopoles in QCD

We propose a new class of defects in QCD which can be viewed as embedded monopoles made of quark and gluon fields. These objects are explicitly gauge invariant and they closely resemble the Nambu monopoles in the standard electroweak model. We argue that the "embedded QCD monopoles" are proliferating in the quark-gluon plasma phase while in the low-temperature hadronic phase the spatial proliferation of these objects is suppressed. At realistic quark masses and zero chemical potential the hadronic and quark-gluon phases are generally believed to be connected by a smooth crossover across which all thermodynamic quantities are nonsingular. We argue that these QCD phases are separated by a well-defined boundary-known as the Kertész line in condensed matter systems-associated with the onset of the proliferation of the embedded QCD monopoles in the quark-gluon plasma phase.

CRITICAL PARAMETERS OF PHASE TRANSITION IN DUAL QCD

Color confinement is studied in dual version of SU (2) color gauge theory using its topological structure and the dynamical breaking of the magnetic symmetry which has been shown to effectively trigger the QCD monopole condensation in a dynamical way. The resulting flux tube structure of the QCD vacuum is explored which has been shown to lead to the perfect dual superconducting nature to the QCD vacuum in its dynamically broken phase. The analysis of the flux tube energy at different hadronic length scales has been shown to lead to the appearance of the strong confinement forces in QCD vacuum at large hadronic distances and an indication for the deconfinement phase at small scales. The analysis of the flux tube energy is then used to compute numerically the critical radius and the critical flux tube density of the phase transition from the flux tube phase to deconfined one inside hadrons. The numerical estimates are shown to be in fairly good agreement with the analytical values. The possible implications of these critical parameters on the formation of QGP as a result of the flux tubes fusion in intermediate energy regime are also discussed.

Gluonic higgs scalar, abelianization and monopoles in QCD - similarity and difference between QCD in the MA gauge and the NAH theory

We study the similarity and the difference between QCD in the maximally abelian (MA) gauge and the nonabelian Higgs (NAH) theory by introducing the ``gluonic Higgs scalar field'' $\vec \phi(x)$ corresponding to the ``color-direction'' of the nonabelian gauge connection. The infrared-relevant gluonic mode in QCD can be extracted by the projection along the color-direction $\vec \phi(x)$ like the NAH theory. This projection is manifestly gauge-invariant, and is mathematically equivalent to the ordinary MA projection. Since $\vec \phi(x)$ obeys the adjoint gauge transformation and is diagonalized in the MA gauge, $\vec \phi(x)$ behaves as the Higgs scalar in the NAH theory, and its hedgehog singularity provides the magnetic monopole in the MA gauge like the NAH theory. We observe this direct correspondence between the monopole appearing in the MA gauge and the hedgehog singularity of $\vec \phi(x)$ in lattice QCD, when the gluon field is continuous as in the SU($N_c$) Landau gauge. In spite of several similarities, QCD in the MA gauge largely differs from the NAH theory in the two points: one is infrared monopole condensation, and the other is infrared enhancement of the abelian correlation due to monopole condensation.

On the dynamics of color magnetic monopoles in full QCD

We present first results on the dynamics of monopoles in full QCD with N f = 2 flavors of dynamical quarks. Among the quantities being studied are the monopole density and the monopole screening length, the static potential as well as the profile of the color electric flux tube. Furthermore, we derive the low-energy effective monopole action.