I analyze the IR fixed point structure of Landau gauge QCD. Precisely the fixed point with a strong kinematic singularity of the quark-gluon vertex that proved crucial for the recently proposed confinement mechanism in the quenched approximation is absent in dynamical QCD. Therefore, the IR singularities do not induce asymptotic quark confinement but the long-range interaction is screened by unquenching loops at scales of the order of the quark mass. This provides the prerequisite for a microscopic description of deconfinement and string breaking. The fixed points determine the qualitative form of the heavy quark potential and may be relevant for hot and dense matter.
A general discussion is presented of the possible symmetries responsible for confinement of color and of their evidence in lattice simulations. The consequences on the phase diagram of $QCD$ are also analyzed.
Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mil…
We summarise an analysis of the infrared regime of Landau gauge QCD by means of a flow equation approach. The infrared behaviour of gluon and ghost propagators is evaluated. The results provide further evidence for the Kugo-Ojima confinement scenario. We also discuss their relation to results obtained with other functional methods as well as the lattice.
We analytically study the relation between quark confinement and spontaneous chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive some formulae for the Polyakov loop, its fluctuations, and the string tension from the Wilson loop. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain wall fermion kernels, respectively. For the confinement quantities, the low-lying Dirac/fermion eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. These relations indicate no direct …
Using the eigen-mode of the QCD Dirac operator $\Slash D=γ^μD^μ$, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculations. Even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking, we find that the Wilson loop obeys the area law, and the string tension or the confinement force is almost unchanged. We find also that the Polyako…
Confinement is explained via field correlators, and the latter are calculated via gluelumps. Behavior of gluelump Green's function at small and large distances yields gluonic condensate and vacuum correlation length respectively and allows to check the consistency of the whole picture.
I start by giving a brief overview over new developments in the area of confinement and topology. As an example for the interrelations between topological objects, instantons at finite temperature are discussed. Then I focus on new insights into the structure of the QCD vacuum obtained through filtering methods, in particular those based on decompositions w.r.t. fermionic eigenmodes.
If the dual Meissner effect due to abelian monopole condensation is the quark confinement mechanism of QCD as suggested in recent Monte-Carlo simulations of lattice QCD, new axial-vector and scalar bosons with the mass of O(1GeV) would appear as physical states which are different from ordinary hadrons and glueballs. The axial-vector boson can not decay into ordinary color-singlet hadrons and glueballs owing to a remainig global discrete permutation symmetry with respect to colors (Weyl symmetry) if the vacuum respects the symmetry as suggested from lattice MC simulations.
The center-stabilized multiflavor QCD* theories formulated on R_3 x S_1 exhibit both Abelian and non-Abelian confinement as a function of the S_1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S_1), we show occurence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r(S_1), the multiflavor theories possess a single phase transition associa…
The theory of confinement based on the stochastic field mechanism, known as the Field Corrleator Method (FCM) is discussed in detail. Experimental and lattice data have accumulated a vast amount of material on the properties of confinement in QCD. We enumerateall these properties as 1)-7), and discuss beyond FCM two existing approaches: monopole based Dual Ginzburg-Landau (DGL) theory,and Gribov-Zwanziger model, from this point of view. It is shown that the FCM satisfies all required criteria. We also prove its selfconsistency; in particular, it is shown that the string tension σ is the only s…
In the lattice QCD formalism, we derive a gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic boundary condition. This analytical relation indicates that low-lying Dirac modes have little contribution to the Polyakov loop. Using lattice QCD simulations, we numerically confirm the analytical relation and the negligible contribution of low-lying Dirac modes to the Polyakov loop at the quenched level, i.e., the Polyakov loop is almost unchanged by remo…
We study in this Letter the origin of the confinement in QCD by analyzing the colour charge of physics states. We derive the colour charge operator in QCD and compare it with the electromagnetic charge operator in QED. It shows that the two charges have very similar structure, but the dynamical properties of the gauge fields are different. The difference between the behaviours of the gauge boson propagator at zero momentum for QCD and that for QED guarantees that there occurs colour confinement in QCD but there is no confinement in QED. We give then a universal relation between the confinement…
We review lattice evidence showing that center-vortex condensation is a serious candidate for the mechanism of colour confinement in quantum chromodynamics.
We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N and N_f\ll N at T\neq 0 and μ\neq 0 is triggered by the drastic change in θbehavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at the value of temperature T=T_c where θdependence experiences a sudden change in behavior[1]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the θdependence) are under complete theoretical control for T>T_c, s…
In this paper we study the properties of QCD at nonzero chiral density $ρ_5$, which is introduced through chiral chemical potential $μ_5$. The study is performed within lattice simulation of QCD with dynamical rooted staggered fermions. We first check that $ρ_5$ is generated at nonzero $μ_5$ and in the chiral limit observe $ρ_5 \sim Λ_{QCD}^2 μ_5$. We also test the possible connection between confinement and topological fluctuations. To this end, we measured the topological susceptibility $χ_{\mbox{\footnotesize top}}$ and string tension $σ$ for various values of $μ_5$. We observed that both s…
The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chir…
In an Abelian projection SU(2) gluodynamics contains Abelian gauge fields (diagonal degrees of freedom) and Abelian matter fields (off-diagonal degrees). The matter fields are essential for the breaking of the adjoint string. We obtain numerically the effective action of the Abelian fields in quenched SU(2) QCD and show that the Abelian matter fields provide an essential contribution to the total action even in the infrared region.
The confinement mechanism proposed earlier by the author is applied to problem of arising the so-called scale $Λ_{QCD}$ within the framework of QCD. The natural physical assumption consists of that $1/Λ_{QCD}\,\sim\,<r>$ where $<r>$ is a characteristic size of hadron (radius of confinement). The above confinement mechanism allows us to calculate $<r>$ for mesons in terms of quark and gluonic degrees of freedom and this permits to conclude that $Λ_{QCD}$ should slightly change from hadron to hadron.
We report on recent progress in understanding confinement of colour in $QCD$ as dual superconductivity of the vacuum. A gauge invariant version of the creation operator of monopoles is constructed whose vacuum expectation value is the order parameter. This order parameter is gauge-invariant from scratch, has no infrared divergences, is finite in the confined phase and vanishes in the deconfined phase. A natural explanation also emerges of why the electric field lines in the flux tubes keep no memory of the colour orientation of the condensing monopoles. A further by-product is that the order p…
In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with $32^4$ at $β$=6.4 (i.e., $a \simeq$ 0.058 fm). We investigate the static quark-antiquark potential $V(r)$, its Abelian part $V_{\rm Abel}(r)$ and its off-diagonal part $V_{\rm off}(r)$, respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., $σ_{\rm Abel} \simeq σ$ for the string tension, on the fine and large-volume lattice. We find als…
An introduction is given into current lattice investigations of the non-perturbative gluon and ghost propagators, in the light of the Gribov-Zwanziger and Kugo-Ojima scenarios of confinement, in the context of results obtained from the non-perturbative Dyson-Schwinger approach in the continuum and in connection with the vortex mechanism of confinement.
Monopole and photon contributions to Wilson loops are calculated using Monte-Carlo simulations of SU(2) QCD in the maximally abelian gauge. The string tensions of SU(2) QCD are well reproduced by extended monopole contributions alone.
We study the gravity dual of four dimensional pure Yang-Mills theory through D4 branes, as proposed by Witten (holographic QCD). In this holographic QCD, it has been widely believed that the confinement phase in the pure Yang-Mills theory corresponds to the AdS D4 soliton in gravity and the deconfinement phase corresponds to the black D4 brane. We inspect this conjecture carefully and show that the correspondence between the black D4 brane and the deconfinement phase is not correct. Instead, by using a slightly different set up, we find an alternative gravity solution called "localized soliton…
We construct a new solution of five-dimensional gravity coupled to a dilaton which encodes essential features of holographic QCD backgrounds dynamically. In particular, it implements linear confinement, i.e. the area law behavior of the Wilson loop, by means of a dynamically deformed anti-de Sitter metric. The predicted square masses of the light-flavored natural-parity mesons and their excitations lie on linear trajectories of approximately universal slope with respect to both radial and spin quantum numbers and are in satisfactory agreement with experimental data.
We study nonperturbative features of QCD using the dual Ginzburg-Landau theory. The color confinement is realized through the dual Higgs mechanism, which is brought by QCD-monopole condensation. We investigate the infrared screening effect on the color confinement due to the light-quark pair creation. By solving the Schwinger-Dyson equation, we find that the dynamical chiral-symmetry breaking is largely brought by the confining force.
We give another derivation of quark confinement in QCD from the viewpoint of the low-energy effective Abelian gauge theory of QCD obtained via Abelian projection. It is based on the recently discovered Berezinskii-Kosterlitz-Thouless phase transition in the four-dimensional Abelian gauge theory. Moreover, we show that there exists a critical gauge coupling constant in QCD, above which confinement set in and below which there is no confinement. In a SU(N) gauge theory with $N_f$ flavored fermions, we argue that this leads to a critical value of fermion flavors $N_f^c$ for the confinement as wel…
Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the centre symmetry is spontaneously broken and colour is liberated. Our findings are supported by lattice gauge simulations for N_c=2...5 and are illustrat…
Based on the permutation group formalism, we present a discrete symmetry algebra in QCD. The discrete algebra is hidden symmetry in QCD, which is manifest only on a space-manifold with non-trivial topology. Quark confinement in the presence of the dynamical quarks is discussed in terms of the discrete symmetry algebra. It is shown that the quark deconfinement phase has the ground state degeneracy depending on the topology of the space, which gives a gauge-invariant distinction between the confinement and deconfinement phases. We also point out that new quantum numbers relating to the fractiona…
An effective monopole action is derived from vacuum configurations after abelian projection in the maximally abelian gauge in $SU(2)$ QCD. Entropy dominance over energy of monopole loops is seen on the renormalized lattice with the spacing $b>b_c\simeq 5.2\times10^{-3} Λ_L^{-1}$ when the physical volume of the system is large enough. QCD confinement may be interpreted as the (dual) Meissner effect due to the monopole condensation.
We study confinement-deconfinement phase transition in a holographic soft-wall QCD model. By solving the Einstein-Maxwell-scalar system analytically, we obtain the phase structure of the black hole backgrounds. We then impose probe open strings in such background to investigate the confinement-deconfinement phase transition from different open string configurations under various temperatures and chemical potentials. Furthermore, we study the Wilson loop by calculating the minimal surface of the probing open string world-sheet and obtain the Cornell potential in confinement phase analytically.
A self-consistent holographic QCD model is proposed which can realize both chiral symmetry breaking and confinement, two most important phenomena of QCD. It is pointed out that the model can accommodate both Regge spectra of hadrons and the linear potential between quarks. The model is formulated in the framework of graviton-dilaton-scalar system, where the dilaton field is dual to the dimension-2 gluon condensate and can lead to the linear confinement, while the scalar field corresponds to the quark anti-quark condensate and can explain the property of chiral dynamics.
Nonperturbative features of QCD are studied using the dual Ginzburg-Landau (DGL) theory with QCD-monopoles. The linear quark potential appears in the QCD-monopole condensed vacuum. We find that QCD-monopole condensation plays an essential role to the dynamical chiral-symmetry breaking. We also investigate the QCD phase transition at finite temperature in the DGL theory.
We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue $λ_n$ such as $λ_n^{N_t-1}$, which behaves as a reduction factor for small $λ_n$. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly sm…
Momentum sum rule in QCD is widely used at high energy colliders. Although the exact form of the confinement potential energy is not known but the confinement potential energy at large distance $r$ can not rise slower than ${\rm ln}(r)$. In this paper we find that if the confinement potential energy at large distance $r$ rises linearly with $r$ (or faster) then the momentum sum rule in QCD is violated at the high energy colliders if we consider the hadron size as infinite. For finite size hadron we find that the momentum sum rule in QCD is violated at the high energy colliders for any form of …
In light of the development of the Gribov issue for pure Euclidean gauge theories and of the recent lattice measurement of soft breaking of the BRST invariance in Yang-Mills theories in the Landau gauge, we consider non-perturbative features in the gauge-interacting matter sector and their relation with general properties of the Faddeev-Popov operator. A signature for BRST breaking in the matter sector is proposed and a local and renormalizable framework is constructed, accommodating this signature and predicting non-perturbative matter propagators that are consistent with available lattice da…
Within the picture of quark confinement as due to a \textit{color event horizon}, and of hadronization as an instance of the Unruh radiation for the strong force, we show here that QCD entropy, evaluated by lattice simulations in the region $T_c < T < 1.3 T_c$, is in reasonable agreement with a melting color event horizon.
On the lattice we study the gauge boson propagator of three dimensional compact QED in Landau gauge at zero and non-zero temperature. The non-perturbative effects are taken into account by the generation of a mass, by an anomalous dimension and by the photon wave function renormalization. All these effects can be attributed to the monopoles: they are absent in the propagator of the singularity-free part of the gauge field. We assess carefully the Gribov copy problem for the propagator and the parameters emerging from the fits.
In a theory with linear confinement, such as QCD, the masses squared m^2 of mesons with high spin S or high radial excitation number n are expected, from semiclassical arguments, to grow linearly with S and n. We show that this behavior can be reproduced within a putative 5-dimensional theory holographically dual to QCD (AdS/QCD). With the assumption that such a dual theory exists and describes highly excited mesons as well, we show that asymptotically linear m^2 spectrum translates into a strong constraint on the INFRARED behavior of that theory. In the simplest model which obeys such a const…
In this paper we develop a phenomenological model inspired by QCD that mimics QCD theory. We use gauge theory in color dielectric medium ($G(ϕ)$) coupled with fermion fields to produce scalar and vector confinement in chromoelectric flux tube scenario. 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 quar…
I propose to reformulate the gauge field theory as the perturbative deformation of a novel topological quantum field theory. It is shown that this reformulation leads to quark confinement in QCD$_4$. Similarly, the fractional charge confinement is also derived in the strong coupling phase of QED$_4$. As a confinement criterion, we use the area decay of the expectation value of the Wilson loop.
The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors $N^{thr}_c$, dividing the theories with essentially different dynamics, is established. For the number of colors $N_c \ll N^{thr}_c$, an anisotropic dynamics of confinement with the confinement scale much less than $Λ_{QCD}$ and a rich spectrum of light glue…
We analyze the question of screening versus confinement in bosonized massless QCD in two dimensions. We deduce the screening behavior of massless $SU(N_c)$ QCD with flavored fundamental fermions and fermions in the adjoint representation. This is done by computing the potential between external quarks as well as by bosonizing also the external sources and analyzing the states of the combined system. We write down novel "non-abelian Schwinger like" solutions of the equations of motion, compute their masses and argue that an exchange of massive modes of this type is associated with the screening…
Dependence of the confinement transition parameters on the fermion content provides information on the mechanism of confinement. Recent progress in lattice gauge theories has allowed to study it for light flavor number $N_f\sim O(10)$ and found this transition to shift toward significantly stronger coupling. We propose an explanation for that: light fermions can occupy the chromo-magnetic monopoles, via zero modes, making them "distinguishable" and unsuitable for Bose-Einstein Condensation. Such dilution of unoccuplied monopoles is compensated by stronger coupling that makes them lighter and m…
The interquark potential is constructed by making use of the new analytic running coupling in QCD. This running coupling arises under ``analytization'' of the renormalization group equation. The rising behavior of the interquark potential at large distances, which provides the quark confinement, is shown explicitly. The estimation of the parameter $Λ_{QCD}$ is obtained.
Colormagnetic confinement as a natural component of the QCD confinement is explained and treated in the framework of the Field Correlator Method. For quarks and gluons in hadrons the effects of the colormagnetic confinement are discussed at zero temperature, where it contributes to the spectrum properties and can create its own bound states, while at nonzero temperature in the EoS of the quark gluon plasma the colormagnetic confinement plays a dominating role. Its properties in the QCD thermodynamics are discussed in detail.
The complete knowledge of a theory is encoded in its correlation functions. Thus non-perturbative effects, like confinement in QCD, is necessarily contained in these correlation functions. As a consequence, a number of confinement scenarios make predictions for the behavior of these correlation functions. Non-perturbative methods, like lattice calculations, permit to calculate the correlation functions and test these predictions. To avoid the entanglement with chiral symmetry breaking and the costs of full fermion simulations, here scalar QCD will be used as a role model, as it is expected tha…
The proton spin crisis remains an unsolved problem in physics. In this paper we find that due to the confinement of partons inside the hadron the angular momentum sum rule in QCD is violated. Hence we find that the non-vanishing angular momentum flux contribution of the partons in QCD should be added to the spin and angular momentum of the partons to solve the proton spin crisis.
We investigate the softwall AdS/CFT model. We specifically looked at the Pomeron, leading Regge contribution to a scattering process and used it to fit deep inelastic scattering data from the HERA collaboration. We find that the model fits the data with much more success than the purely conformal case, and find similar success to previous confinement models.
Using the effective potential formalism, we study dynamical chiral symmetry breaking (D$χ$SB) in the dual Ginzburg-Landau (DGL) theory, where the color confinement is brought by monopole condensation. The effective potential as a function of infrared quark mass is found to have double-well structure, which leads to spontaneous breaking of chiral symmetry. To examine the role of confinement, we divide the effective potential into the confinement part and others, which correspond to the confinement term and other (Yukawa, Coulomb) terms of the gluon propagator in the DGL theory. It is found that…
We present an attempt towards constructing relativistic quark-gluon quasi-potentials from QCD using Unitary Clothing Transformations (UCT) approach. The brief review of the UCT method is given. Starting from a simplified model of QCD hamiltonian (H), we define the 'color-clothed' representation (CCR) of H. In this representaion, it is required that only color-singlet states are the eigenstates of the H. In CCR, H contains the family of quantum relativistic potentials acting between 'color clothed' quarks and gluons. Simultaneously, newly defined quarks acquire new masses (expected to be close …
The situation with asymptotically flat gravitating spinor field solutions is considered. It is supposed that the problem of constructing these solutions is connected with confinement problem in quantum chromodynamics. It is argued that in both cases we must use a nonperturbative quantum technique.
Recently there have been proposals to understand features of QCD such as confinement and chiral symmetry breaking by considering supersymmetric versions of the theory with various patterns of soft breaking. In this note we recall that with small soft breakings, SUSY QCD is suggestive of observed features of real QCD. But we outline some of the challenges to establishing these features of the theory with large soft breakings. It appears difficult to argue for confinement or chiral symmetry breaking; at best, one can say that {\it if} the non-supersymmetric theory does not confine and/or break c…
We argue that lattice calculations of the $η'$ mass in QCD with $N_c=2$ colors performed at non-zero baryon chemical potential can be used to study the mechanism responsible for the mass of the $η'$. QCD with two colors is an ideal laboratory because it exhibits confinement, chiral symmetry breaking and a would-be $U(1)_A$ Goldstone boson at all densities. Since the instanton density and the confinement scale vary with density in a very different way, instantons are clearly distinguishable from other possible mechanisms. There is an instanton prediction for the $η'$ mass at large density that …
The infrared behaviour of the gluon and ghost propagators in Landau gauge QCD is reviewed. The Kugo-Ojima confinement criterion and the Gribov-Zwanziger horizon condition result from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement with corresponding lattice data obtained recently. The resulting running coupling approaches a fix point in the infrared, $α(0) = 8.…
We investigate the infrared behaviour of gluon and ghost propagators in Landau gauge QCD by means of an exact renormalisation group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimisation procedure is devised to remove residual regulator dependences. In Landau gauge QCD this framework is used to determine the infrared leading terms of the propagators. The results support the Kugo-Ojima confinement scenario. Possible extensions are discussed.
An expression for the exact (nonperturbative) effective action of $N$=1 supersymmetric gauge theories is proposed, supposing, that all particles except for the gauge bosons are massive. Analysis of its form shows, that instanton effects in the supersymmetric theories can lead to the quark confinement. The typical scale of confinement in MSSM QCD, calculated from the first principles, is in agreement with the experimental data. The proposed explanation is quite different from the dual Higgs mechanism.
We study confinement and chiral symmetry breaking phase transitions for QCD and supersymmetric QCD. The method is based on some justified assumption regarding the behavior of the Green function relevant for the potential between two charges or a gap equation. We determine the number of flavors at which the transitions to confinement and chiral symmetry breaking take place. We find that whereas for chiral symmetry breaking the results are in perfect agreement with those in the literature for confinement the situation is more complex.
