$Q\bar{Q}$ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci-Ferrari type, the possibility of a gluon condensation $\langle A_μ^+A_μ^-\rangle$ in low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales $r_c$ and $\tilde{R}_0$. The meanings of these scales are clarified. We also show that the Cornell potential that fits well to this confining potential is obtained by taking these scales into account.
The recently obtained solutions of the Dirac equation in the confining SU(3)-Yang-Mills field in Minkowski spacetime are applied to describe the energy spectrum of charmonium. The nonrelativistic limit is considered for the relativistic effects to be estimated in a self-consistent way and it is shown that the given effects could be extremely important for both the energy spectrum and the confinement mechanism.
The recently obtained solutions of Dirac equation in the confining SU(3)-Yang-Mills field in Minkowski spacetime are applied to describe the energy spectra of quarkonia (charmonium and bottomonium). The nonrelativistic limit is considered for the relativistic effects to be estimated in a self-consistent way and it is shown that the given effects are extremely important for both the energy spectra and the confinement mechanism.
The estimates of the gluon concentrations in the classical SU(3)-Yang-Mills field modelling confinement are given for the first three states of charmonium whose spectrum is tuned by calculating electromagnetic transitions among the mentioned levels in dipole approximation. For comparison the corresponding estimates for the photon concentration in the ground state of positronium (parapositronium and orthopositronium) are also adduced.
Almost massless mesons created at the condensation scale of extra nonabelian gauge group can be candidates of dark energy source. This can be another motivation for introducing an additional confining force.
We show that the QCD vacuum (without dynamical quarks) is a dual superconductor at least in the low-energy region in the sense that monopole condensation does really occur. In fact, we derive the dual Ginzburg-Landau theory (i.e., dual Abelian Higgs model) directly from the SU(2) Yang-Mills theory by adopting the maximal Abelian gauge. The dual superconductor can be on the border between type II and type I, excluding the London limit. The masses of the dual Abelian gauge field is expressed by the Yang-Mills gauge coupling constant and the mass of the off-diagonal gluon of the original Yang-Mil…
The black hole physics techniques and results are applied to find the set of the exact solutions of the SU(3)-Yang-Mills equations in Minkowski spacetime in the Lorentz gauge. All the solutions contain only the Coulomb-like or linear in $r$ components of SU(3)-connection. This allows one to obtain some possible exact and approximate solutions of the corresponding Dirac equation that can describe the relativistic bound states. Possible application to the relativistic models of mesons is also outlined.
It is proven that dual superconductivity of QCD vacuum in the confining phase is an intinsic property, independent on the choice of the abelian projection used to define the monopoles.
Structure of exact solutions modelling confinement is discussed for SU(3)-Yang-Mills equations and uniqueness of such confining solutions is proved in a certain sense. Relationship of the obtained results to QCD and the confinement mechanism is considered. Incidentally the Wilson confinement criterion for the found solutions is verified and also numerical estimates for strength of magnetic colour field responsible for linear confinement are adduced in the ground state of charmonium.
We consider a general framework to study holographically the dynamics of fundamental quarks in a confining gauge theory. Flavors are introduced by placing a set of (coincident) branes and antibranes on a background dual to a confining color theory. The spectrum contains an open string tachyon and its condensation describes the U(N_f)_L x U(N_f)_R -> U(N_f)_V symmetry breaking. By studying worldvolume gauge transformations of the flavor brane action, we obtain the QCD global anomalies and an IR condition that allows to fix the quark condensate in terms of the quark mass. We find the expected N_…
We study the structure of the confining string in Yang-Mills theory using the method of the field strength correlators. The method allows us to demonstrate that both the local fluctuations of the topological charge and the gluon condensate are suppressed in the vicinity of the string axis in agreement with results of lattice simulations.
We discuss relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the dual formulation which involves higher dimensions. We try to bridge these two approaches to the confinement, let it be on a rudimentary level. We review lattice data on low-dimensional defects, that is monopoles, center vortices, topological defects. There is certain resemblance to dual strings, domain walls, introduced in large-N Yang-Mills theories.
We discuss thermodynamic properties of open confining strings introduced via static sources in the vacuum of Yang-Mills theory. We derive new sum rules for the chromoelectric and chromomagnetic condensates and use them to show that the presence of the confining string lowers the gluonic pressure in the bulk of the system. The pressure deficit of the gluon plasma is related to the potential energy in the system of heavy quarks and anti-quarks in the plasma.
The dynamical mass generation for gluons is discussed in Euclidean Yang-Mills theories supplemented with a renormalizable mass term. The mass parameter is not free, being determined in a self-consistent way through a gap equation which obeys the renormalization group. The example of the Landau gauge is worked out explicitly at one loop order. A few remarks on the issue of the unitarity are provided.
We study SU(2) three-dimensional Yang-Mills theories in presence of Higgs fields in the light of the Gribov phenomenon. By restricting the domain of integration in the functional integral to the first Gribov horizon, we are able to discuss a kind of transition between the Higgs and the confining phase in a semi-classical approximation. Both adjoint and fundamental representation for the Higgs field are considered, leading to a different phase structure.
By superposition of regular gauge instantons or merons, ensembles of gauge fields are constructed which describe the confining phase of SU(2) Yang-Mills theory. Various properties of the Wilson loops, the gluon condensate and the topological susceptibility are found to be in qualitative agreement with phenomenology or results of lattice calculations. Limitations in the application to the glueball spectrum and small size Wilson loops are discussed.
We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)-d SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multi-level algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher order terms in the effective string action are calculated analytically. They accurately fit the numerical data.
The exact nonperturbative confining solutions of the SU(3)-Yang-Mills equations recently obtained by author in Minkowski spacetime with the help of the black hole theory techniques are analysed and on the basis of them the gluon propagator corresponding to linear confinement at large distances (small momenta) is constructed in a nonperturbative way. At small distances (large momenta) the resulting propagator passes on to the standard (nonperturbative) gluon propagator used in the perturbative quantum chromodynamics (QCD). The results suggest some scenario of linear confinement for mesons and q…
We present a numerical method to compute path integrals in effective SU(2) Yang-Mills theories. The basic idea is to approximate the Yang-Mills path integral by summing over all gauge field configurations, which can be represented as a linear superposition of a small number of localized building blocks. With a suitable choice of building blocks many essential features of SU(2) Yang-Mills theory can be reproduced, particularly confinement. The analysis of our results leads to the conclusion that topological charge as well as extended structures are essential elements of confining gauge field co…
It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics (QCD). But hints of these features can also be observed at purely classic levels. For this purpose we need to find solutions to the colorly-sourceful Yang-Mills equations with both confining and asymptotic freedom features. We provide such a solution in this paper which at the near-source region is of serial form, while at the far-away region is approximately expressed through simple elementary functions. From the solution, we derive out a classically non-perturbative beta function describing the …
The logarithmic broadening predicted by the systematic low-energy effective field theory for the confining string has recently been verified in numerical simulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The same effective theory predicts linear broadening of the string at low non-zero temperature. In this paper, we verify this prediction by comparison with very precise Monte Carlo data. The comparison involves no additional adjustable parameters, because the low-energy constants of the effective theory have already been fixed at zero temperature. It yields very good …
We review some difficulties of the standard picture of confining fields which are viewed usually as `mild', or quasiclassical field configurations. The paradoxes are naturally resolved by recent lattice observations of selftuned fluctuations which exhibit both ultraviolet and infrared scales. The ultraviolet scale is provided by the lattice spacing and is manifested in the non-Abelian action density associated with the fluctuations while the physical scale is exhibited by their geometrical characteristics. The data might suggest existence of a dual description of Yang-Mills theories on the fun…
In the framework of the functional renormalization group, we reexamine the stability of the Yang-Mills vacuum with a chromomagnetic condensation. We show that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous chromomagnetic condensation disappears in the $SU(2)$ Yang-Mills theory. As a physical mechanism for maintaining the stability even for the small infrared cutoff, we argue that dynamical gluon mass generation occurs due to a BRST-invariant vacuum condensate of mass dimension-two, which is related to two-gluon bound states identified with glueballs. These results supp…
We consider the dual Yang-Mills theory which shows some kind of confinement at large distances. In the static system of the test color charges an analytic expression for the string tension is derived.
It is showed that potentials derived from classical solutions of the SU(3) Yang-Mills theory can provide confining potentials that reproduce the heavy quarkonium spectrum within the same level of precision as the Cornell potential.
Chromomagnetic condensation and perturbative confinement induced by imaginary rotation in SU(2) Yang-Mills Theory
School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
We study the vacuum structure and dyon spectrum of N=2 supersymmetric gauge theory in four dimensions, with gauge group SU(2). The theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and dyon masses and the metric on the moduli space of vacua. The description involves a version of Olive-Montonen electric-magnetic duality. The ``strongly coupled'' vacuum turns out to be a weakly coupled theory of monopoles, and with a suitable perturbation confinement is described by monopole co…
In this work, we propose a $3D$ ensemble measure for center-vortex worldlines and chains equipped with non-Abelian degrees of freedom. We derive an effective field description for the center-element average where the vortices get represented by $N$ flavors of effective Higgs fields transforming in the fundamental representation. This field content is required to accommodate fusion rules where $N$ vortices can be created out of the vacuum. The inclusion of the chain sector, formed by center-vortex worldlines attached to pointlike defects, leads to a discrete set of $Z(N)$ vacua. This type of SS…
Generalization of QCD motivated classical SU(2) Yang--Mills theory coupled to the scalar field is discussed. The massive scalar field, corresponding the scalar glueball, provides a confining potential for static, point-like, external sources. In case of massless scalar field screening solutions are found. However, there is a confining sector as well. Both, massive and massless confining solutions are compared with phenomenological potentials. The case of non-dynamical permittivity is also discussed.
We provide a simple low energy description of recombination of intersecting D-branes using super Yang-Mills theory. The recombination is realized by condensation of an off-diagonal tachyonic fluctuation localized at the intersecting point. The recombination process is equivalent to brane-antibrane annihilation, thus our result confirms Sen's conjecture on tachyon condensation, although we work in the super Yang-Mills theory whose energy scale is much lower than alpha'. We also discuss the decay width of non-parallelly separated D-branes.
We study the drag force of a relativistic heavy quark using a holographic QCD model with conformal invariance broken by a background dilaton. We analyze the effects of chemical potential and confining scale on this quantity, respectively. It is shown that the drag force in this model is larger than that of $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) plasma. In particular, the inclusion of the chemical potential and confining scale both enhance the drag force, in agreement with earlier findings. Also, we discuss how chemical potential and confining scale influence the diffusion coefficient.
We discuss within the weak-field approximation and the derivative expansion how the area law of the Wilson loop follows directly from the vacuum condensate of mass dimension 2, i.e., simultaneous Bose-Einstein condensation of gluon pair and ghost-antighost pair. Such a novel vacuum condensate was recently claimed to exist as the non-vanishing vacuum expectation value of a BRST-invariant composite operator of mass dimension 2. First of all, we use a version of the non-Abelian Stokes theorem to rewrite the Wilson loop line integral to a surface integral. Then we convert the Yang-Mills theory wit…
We propose an analytical approach to SU(2) Yang-Mills thermodynamics. The existence of a macroscopic and rigid adjoint Higgs field, generated by dilute trivial-holonomy calorons at large temperature $T$ (electric phase), implies a twofold degeneracy of the ground state which signals a broken electric $Z_2$ symmetry. A finite energy density $\propto T$ of the ground state arises due to caloron interaction. An evolution equation for the effective gauge coupling, derived from thermodynamical self-consistency, predicts a second-order like transition (seen in lattice simulations) at $T_c$ to a phas…
We present a first numerical evidence for the existence of a novel magnetic condensate proposed recently by one of the authors in SU(2) Yang-Mills theory. In our framework, the spontaneously generated color magnetic field identified with the Savvidy vacuum has the microscopic origin and is a consequence of the intrinsic dynamics of the Yang-Mills theory. It strongly suggests the Nielsen--Olesen instability of the Savvidy vacuum disappears and the stability is restored without the need of the Copenhagen vacuum. The implications to the Faddeev-Skyrme model are also discussed. These results are o…
We investigate the connection between Color Confinement and thermal Abelian monopoles populating the deconfined phase of SU(2) Yang-Mills theory, by studying how the statistical properties of the monopole ensemble change as the confinement/deconfinement temperature is approached from above. In particular we study the distribution of monopole currents with multiple wrappings in the Euclidean time direction, corresponding to two or more particle permutations, and show that multiple wrappings increase as the deconfinement temperature is approached from above, in a way compatible with a condensati…
We show that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous chromomagnetic condensation disappears in the framework of the functional renormalization group. This result follows from our observations: (i) the vanishing imaginary part of the effective average action is realized for arbitrary infrared cutoff as a novel fixed point solution of the flow equation for the complex-valued effective average action and (ii) an approximate analytical solution for the effective average action is obtained without the pure imaginary part for large infrared cutoff. This result suggest…
The glueballs lead to gluon and QCD monopole condensations as by-products of color confinement. A color dielectric function $G(|ϕ|)$ coupled with Abelian gauge field is properly defined to mediate the glueball interactions at confining regime after {\it spontaneous symmetry breaking} (SSB) of the gauge symmetry. The particles are expected to form through quark gluon plasma (QGP) hadronization phase where the free quarks and gluons start clamping together to form hadrons. The QCD-like vacuum $\langleη^2m_η^2F^{μν}F_{μν}\rangle$, confining potential $V_c(r)$, string tension $σ$, penetration dept…
One can define generalized models of gaugino condensation as theories which dynamically break a discrete R-symmetry, but do not break supersymmetry. We consider general examples consisting of gauge and matter fields, and the minimal number of gauge singlet fields to avoid flat directions in the potential. We explore which R-symmetries can arise, and their spontaneous breaking. In general, we find that the discrete symmetry is $\mathbb{Z}_{2b_0R}$ and the number of supersymmetric vacua is $b_0$, where $b_0$ is the coefficient of the one-loop beta function. Results are presented for various grou…
We investigate the infrared (strong-coupling) regime of SU(N)-Yang-Mills theory on a self-dual background. We present an evaluation of the full effective potential for the field strength invariant F_{μν}F^{μν} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the beta function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators. Consistency between both gauges in the infrared …
Domain Walls From Confining Bubbles: $SU(N_{c})$ Yang Mills at Finite $θ$
SISSA, International School for Advanced Studies（国际高等研究院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU, Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Dipartimento di Fisica, Università di Trieste（的里雅斯特大学物理系）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
We analyze the leading Lyapunov exponents of SU(2) Yang-Mills field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We find that configurations in the strong coupling phase at finite temperature are substantially more chaotic than in deconfinement.
We study some features of the confining string connecting a quark-anti-quark pair in Yang-Mills theory. Monte Carlo investigations of the flux tube between two static quarks in the fundamental representation show that its thickness increases with the separation of the sources. The collected numerical data in (2+1)-d SU(2) Yang-Mills theory are in very good quantitative agreement with the next-to-leading order formula derived from the systematic low-energy effective theory of the confining string. At zero temperature, we observe the predicted logarithmic broadening. At finite and low temperatur…
We exhibit $N=1$ supersymmetric field theories in confining, Coulomb and Higgs phases. The superpotential and the gauge kinetic terms are holomorphic and can be determined exactly in the various phases. The Coulomb phase generically has points with massless monopoles. When they condense, the theory undergoes a phase transition to a confining phase. When there are points in the Coulomb phase with massless electric charges, their condensation leads to a transition to a Higgs phase. When the Higgs and confinement phases are distinct, we expect to find massless interacting gluons at the transition…
I reexamine the phenomena of the chromomagnetic gluon condensation in Yang-Mills theory. The extension of the Heisenberg-Euler Lagrangian to the Yang-Mills theory allows to calculate the effective action, the energy-momentum tensor and demonstrate that the energy density curve crosses the zero energy level of the perturbative vacuum state at nonzero angle and continuously enters to the negative energy density region. At the crossing point and further down the effective coupling constant is small and demonstrate that the true vacuum state of the Yang-Mills theory is below the perturbative vacuu…
We consider the Hamiltonian formulation of Yang-Mills theory in the Coulomb gauge and apply the recently developed technique of Hamiltonian flows. We formulate a flow equation for the color Coulomb potential which allows for a scaling solution that results in an almost linearly rising confining potential.
An effective theory based on ensembles of either regular gauge instantons or merons is shown to produce confinement in SU(2) Yang-Mills theory. When the scale is set by the string tension, the action density, topological susceptibility and low-lying glueball spectrum are similar to those arising in lattice QCD. The physical mechanism producing confinement is explained, and a number of analytical insights into the effective theory are presented.
We present an analytic nonperturbative solution of the Yakubovsky equation for tetraquark states in the case of equal separations and energies, and demonstrate a direct connection between the tetraquark confinement potential and the temporal gluon propagator. To this end we employ a leading-order heavy quark mass expansion of the Coulomb gauge QCD action, and use the dressed two-point functions of the Yang-Mills sector only. As a result we find a bound state energy that rises linear with distance and a string tension twice as large as in a $q\bar{q}$-system.
The pseudoparticle approach is a numerical method to approximate path integrals in SU(2) Yang-Mills theory. Path integrals are computed by summing over all gauge field configurations, which can be represented by a linear superposition of a small number of pseudoparticles with amplitudes and color orientations as degrees of freedom. By comparing different pseudoparticle ensembles we determine properties of confining gauge field configurations. Our results indicate the importance of long range interactions between pseudoparticles and of non trivial topological properties.
Monte Carlo simulations are performed in a five-dimensional lattice SU(2) Yang-Mills theory with a compactified extra dimension, and scaling laws are studied. Our simulations indicate that as the compactification radius $R$ decreases, the confining phase spreads more and more to the weak coupling regime, and the effective dimension of the theory changes gradually from five to four. Our simulations also indicate that the limit $a_4 to 0$ with $R/a_4$ kept fixed exists both in the confining and deconfining phases if $R/a_4$ is small enough, where $a_4$ is the lattice spacing in the four-dimensio…
We analyze the effect of an isospin chemical potential μ_I in the Sakai-Sugimoto model, which is the string dual of a confining gauge theory related to large N_c QCD, at temperatures below the chiral symmetry restoration temperature. For small chemical potentials we show that the results agree with expectations from the low-energy chiral Lagrangian, and the charged pion condenses. When the chemical potential reaches a critical value μ_I = μ_{crit} ~ 1.7 m_ρ, the lowest vector meson (the "rho meson") becomes massless, and it condenses (in addition to the pion condensate) for μ_I > μ_{crit}. Thi…
The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the Dyson-Schwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghost-gluon vertex.
For the four-dimensional SU(N) Euclidean Yang-Mills theory in the Landau gauge, we present two sets of gauge field configurations that satisfy the Euclidean equations of motion. These configurations generate four-dimensional chromo-field flux sheets whose spatial cross sections are three-dimensional chromo-field flux tubes. In lattice simulations, they may be detected as center vortices. The first set of gauge field configurations generates chromo-electric flux tubes that should contribute to a chromo-electric flux tube between two static color charges. The string tension for two static color …
We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU(2) Yang-Mills theory under the Cho--Faddeev--Niemi decomposition. We point out that the generated gluon mass can cure the instability of the Savvidy vacuum. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential. This enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which suggests the dual superconduc…
We analyze the Wilson loop for a pure Yang-Mills theory, using a decoupling solution in close agreement with lattice computations. At one-gluon exchange level it is seen that the potential cannot yield a linear rising contribution as expected for a confining theory. Next-to-leading order correction gives rise to a quartic term for momenta in the gluon propagator that, in agreement with Gribov's view, yields a linear confining term. This correction is due to a two-loop or sunrise integral that we need to evaluate in the low-momenta limit. In the infrared regime, the physical consistency of the …
We show a constantly accelerated quark as a string solution of the Nambu-Goto action, which is embedded in the bulk background dual to the $\cal{N}$ $=2$ supersymmetric confining Yang-Mills theory. The induced metric of the world sheet for this string solution has an event horizon specified by the fifth coordinate. By an extended Rindler transformation proposed by Xiao, we move to the comoving frame of the accelerated quark-string. Then we find that this horizon is transferred to the event horizon of the bulk and the causal part of the accelerated quark is transformed to a static free-quark in…
A generalized Faddeev-Niemi ansatz for the gluon field is discussed. In its simplest parametrization, the ansatz allows a solution of the classical SU(3) Yang-Mills equations. From these solutions a confining potential for heavy quarkonia is defined. The investigation of charmonium spectra proves that the potential is able to reproduce the experimental spectra at the level of 3%. Moreover, charmonium leptonic and strong decays are investigated. The results are in fair agreement with experimental figures and are in line with other quark model calculations.
