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 fractional quantum Hall effect exist in the deconfinement phase.
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.
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 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 for…
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.
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 use lattice QCD simulations to test some of the predictions of proposed AdS/QCD (holographic) duals for QCD. In particular, these duals predict that the scale of chiral symmetry breaking ($χ$SB) can be varied independently from that of confinement, with the proviso that the scale of $χ$SB cannot be longer than that of confinement. We simulate lattice QCD with 2 quarks in the fundamental representation of colour and with additional 4-fermion interactions (suggested by AdS/QCD), at finite temperatures. For sufficiently strong 4-fermion interactions, the deconfinement and $χ$SB transitions occ…
We give a new criterion of quark confinement/deconfinement by deriving a low-energy effective theory of QCD. The effective theory can explain Abelian dominance in low-energy physics of QCD, especially, quark confinement. Finally, we apply the above criterion to the large flavor QCD and discuss its phase structure. The result suggests the existence of conformal phase.
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.
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 spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures $T=220-380$ MeV. We measure the correlators of spin-one ($J=1$) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries of QCD implies degeneracies in vector--axial-vector ($SU(2)_L \times SU(2)_R$) and tensor--axial-tensor ($U(1)_A$) pairs, which are indeed observed at temperatures above $T_c$. Moreover, we observe an approximate degeneracy of all $J=1$ correlators with incre…
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…
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…
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…
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.
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…
Gauge field configurations appropriate for the infrared region of QCD are proposed. Using the usual QCD action, confinement is realized as in the London theory of Meissner effect.
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 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.
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.
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.
We consider the degeneracy between the Regge slope of mesons and baryons in QCD. We argue that within the "orientifold large-N approximation" asymptotically massive mesons and baryons become supersymmetric partners and hence degenerate. To this end, we generalize QCD by a SU(N) theory with a quark in the two-index antisymmetric representation. We show that in this framework the meson is represented by an oriented bosonic QCD-string and the baryon is represented by an un-oriented fermionic QCD-string. At large-N, due to an equivalence with super Yang-Mills, the tensions of the bosonic and the f…
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.
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…
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…
We give an outline of a recent proof that the low-energy effective gauge theory exhibiting quark confinement due to magnetic monopole condensation can be derived from QCD without any specific assumption. We emphasize that the low-energy effective abelian gauge theories obtained here give the dual description of the same physics in the low-energy region. They show that the QCD vacuum is nothing but the dual (type II) superconductor.
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.
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 calculation on $6^4$ at $β$=5.6. 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 slope parameter corresponding to the string tension or the confinement …
We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial $S^1 \times \R^3$. The absence of thermal fluctuations, and the fact that quantum fluctuations favoring the vacuum with unbroken center symmetry in a weakly coupled regime renders the interesting dynamics of these theories analytically calculable. Confinement, the area law behavior for large Wilson loops, and the generation of the mass gap in the gluonic sector are shown analytically. By abelian duality transformation, the long distance effective theory of QCD is ma…
We investigate the relevant gluon-momentum region for confinement in lattice QCD on $16^4$ at $β$=5.7, 5.8 and 6.0, based on the Fourier expansion. We find that the string tension $σ$, i.e., the confining force, is almost unchanged even after removing the high-momentum gluon component above 1.5GeV in the Landau gauge. In fact, the confinement property originates from the low-momentum gluon component below 1.5GeV, which is the upper limit to contribute to $σ$. In the relevant region, smaller gluon momentum component is more important for confinement. Next, we develop a manifestly gauge-covarian…
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.
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…
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…
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…
We present analytical methods for investigating the interaction of two heavy quarks in QCD_3 using the effective action approach. Our findings result in explicit expressions for the static potentials in QCD_3 for long and short distances. With regard to confinement, our conclusion reflects many features found in the more realistic world of QCD_4.
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…
An exactly soluble non-perturbative model of the pure gauge QCD is derived as a weak coupling limit of the lattice theory in plaquette formulation. The model represents QCD as a theory of the weakly interacting field strength fluxes. The area law behavior of the Wilson loop average is a direct result of this representation: the total flux through macroscopic loop is the additive (due to the weakness of the interaction) function of the elementary fluxes. The compactness of the gauge group is shown to be the factor which prevents the elementary fluxes contributions from cancellation. There is no…
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.
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.
Suggested holographic duals of QCD, based on AdS/CFT duality, predict that one should be able to vary the scales of colour confinement and chiral-symmetry breaking independently. Furthermore they suggest that such independent variation of scales can be achieved by the inclusion of extra 4-fermion interactions in QCD. We simulate lattice QCD with such extra 4-fermion terms at finite temperatures and show that for strong enough 4-fermion couplings the deconfinement transition occurs at a lower temperature than the chiral-symmetry restoration transition. Moreover the separation of these transitio…
Phenomenological model for confining Lagrangian based on the perfect dia-electric property of the vacuum of QCD, proposed by Kogut-Susskind and by 't Hooft, is derived by the stability of the condensed vacuum.
We present a strong evidence for the magnetic confinement in QCD by demonstrating that the one loop effective action of SU(2) QCD induces a dynamical symmetry breaking thorugh the monopole condensation, which could induce the dual Meissner effect and guarantee the confinement of color in the non-Abelian gauge theory. The result is obtained by separating the topological degrees which describes the non-Abelian monopoles from the dynamical degrees of the potential, and integrating out all the dynamical degrees of QCD.
We study the relation between quark confinement and spontaneous chiral-symmetry breaking directly in QCD. In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $λ_n$, i.e., $\langle L_P \rangle \propto \sum_n λ_n^{N_t -1} \langle n|\hat U_4|n \rangle$, on a temporally odd-number lattice, where the temporal lattice size $N_t$ is odd. Here, $|n \rangle$ denotes the Dirac eigenmode, i.e., $\not D|n \rangle=iλ_n|n \rangle$, and $\hat U_4$ the temporal link-variable operator. We here use an ordinary squar…
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.
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 …
I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribov's confinement scenario is realized in this gauge. For this purpose I will discuss in detail the emergence of the horizon condition and the Coulomb string tension. I will show that both are induced by center vortex gauge field configurations, which establish the connection between Gribov's confinement scenario and the center vortex picture of confinement. I will then extend the Hamiltonian approach to QCD in Coulomb gauge to finite temperatures, first by the usual grand canonical ensemble an…
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…
In supersymmetric gluodynamics (N=1 super-Yang-Mills theory) we show that the spectral functions induced by the nonchiral operator Tr G_{αβ} \barλ^2 are fully degenerate in the J^{PC}=1^{\pm -} channels. The above operator is related to N=1/2 generalization of SUSY. Using the planar equivalence, this translates into the statement of degeneracy between the mesons produced from the vacuum by the operators (\bar Ψ\vec EΨ+ i\bar Ψ\vec B γ^5Ψ) and (\bar Ψ\vec BΨ- i\bar Ψ\vec E γ^5Ψ) in one-flavor QCD, up to 1/N corrections. Here Ψis the quark field, and \vec E ,\vec B are chromoelectric/chromomagne…
We identify two distinct, complementary gauge field configurations for QCD with SU(2) gauge group, one (instanton-like configurations) having to do with chiral symmetry breaking but not with confinement, the other (regularized Wu-Yang monopoles) very likely responsible for confinement but unrelated to chiral symmetry breaking. Our argument is based on a semiclassical analysis of fermion zero modes in these backgrounds, made by use of a gauge field decomposition recently introduced by Faddeev and Niemi. Our result suggests that the two principal dynamical phenomena in QCD, confinement and chira…
The problem of the phase transition of a Z(3) spin system is a complex issue. A numerical simulation in the framework of the mean field theory using the Metropolis algorithm reveals: (a) the existence of second order phase transition with a degenerated critical point which could be considered as a state of resonance (b) hysteresis phenomena which are accompanied with tricritical crossover around the end point of first order transition. Based on these results we propose a scenario about confinement-deconfinement phase transition in SU(3) symmetry of color QCD which, as it is known, has the same…
