The dynamical holographic QCD method for hadron physics and QCD matter

In this paper we present a short overview on the dynamical holographic QCD (DhQCD) method for hadron physics and QCD matter. The five-dimensional DhQCD model is constructed in the graviton-dilaton-scalar framework with the dilaton background field Φ and the scalar field X dual to the gluon condensate and the chiral condensate operator thus can represent the gluodynamics (linear confinement) and chiral dynamics (chiral symmetry breaking), respectively. The dilaton background field and the scalar field are a function of the 5th dimension, which plays the role of the energy scale, in this way, the DhQCD model can resemble the renormalization group from ultraviolet (UV) to infrared (IR). By solving the Einstein equation, the metric structure at IR is automatically deformed by the nonperturbative gluon condensation and chiral condensation in the vacuum. We review the results on the hadron spectra including the glueball spectra, the light/heavy meson spectra, as well as on QCD phase transitions, and thermodynamical as well as transport properties in the framework of the DhQCD model.     

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. PACS: 12.38.Aw; 11.30.-j; 14.80.Hv; 12.39.Mk An erratum to this article is available at .     

Gluon condensates at finite baryon densities and temperature

We derive here the equation of state for quark matter with a nontrivial vacuum structure in QCD at finite temperature and baryon density. Using thermofield dynamics, the parameters of thermal vacuum and the gluon condensate function are determined through minimisation of the thermodynamic potential, along with a self-consistent determination of the effective gluon and quark masses. The scale parameter for the gluon condensates is related to the SVZ parameter in the context of QCD sum rules at zero temperature. With inclusion of quarks in the thermal vacuum the critical temperature at which the gluon condensate vanishes decreases as compared to that containing only gluons. At zero temperature, we similarly obtain the critical baryon density for the same to be about 0.36 fm^?3.     

Quark Gluon Condensate,Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work. The structure of non-local quark vacuum condensate, values of various local quark and gluon vacuum condensates, quark-gluon mixed vacuum condensate, quark and gluon virtuality in QCD vacuum state, quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in “rainbow” approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters. Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature, and many other theoretical calculations. The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations. This work is centrally important for studying non-perturbative QCD, and has many important applications both in particle and nuclear physics.     

Long-Range Behavior of Dual-Restricted QCD Vacuum

We analyze the geometrical structure of the local non-Abelian gauge theory in terms of the magnetic symmetry, using the resemblance between the non-Abelian gauge formulations and Einstein's theory of gravitation in a higher dimensional unified space. The mathematical foundation of dual QCD in fiber bundle form is then discussed and used for the analysis of the important problem of color confinement in QCD. The associated Lagrangian formulation in magnetic gauge is shown to lead to dual dynamics due to the emergence of the topological charges of magnetic nature. The dynamical breaking of magnetic symmetry is shown to lead to the magnetic condensation of the QCD vacuum. A state of the dual superconductivity in the QCD vacuum is then shown to evolve which ultimately pushes the QCD vacuum to the confining phase. The flux tube structure of the magnetically condensed QCD vacuum is analyzed by computing the asymptotic string solutions of the field equations. The energy content of such confining structures is computed and analyzed in terms of its logarithmic and linear nature.     

The quark condensate in the bag-like QCD vacuum

The quark condensate in the bag model of the QCD vacuum is discussed. It is shown that the systems with J^PC=0⁺⁺ quantum numbers produce a much deeper minimum in the energy density than the recently suggested glueball condensate. Some consequences of this observation are pointed out.     

Chiral symmetry breaking and monopole condensation in QCD

We show that, in the dual superconductor picture of the QCD vacuum, the presence of the monopole condensate inevitably leads to the breaking of the chiral symmetry.     

Abelian duality, confinement, and chiral-symmetry breaking in a SU(2) QCD-like theory

We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial S(1) x R(3). The absence of thermal fluctuations, and the fact that quantum fluctuations favor the vacuum with unbroken center symmetry in a weakly coupled regime, renders the interesting dynamics of these theories analytically calculable. Confinement and the generation of the mass gap in the gluonic sector are shown analytically. In this regime, theory exhibits confinement without continuous chiral-symmetry breaking. However, a flavor singlet chiral condensate (which breaks a discrete chiral symmetry) persists at arbitrarily small S(1). Under certain reasonable assumptions, we show that the theory exhibits a zero temperature chiral phase transition in the absence of any change in spatial center symmetry realizations.     

瞬子效应在0++胶球的QCD求和规则中的作用

利用包含瞬子效应的QCD求和规则计算了0⁺⁺胶球的质量上限,结果为1.3GeV.还探讨了变动瞬子参量时对QCD求和规则的影响,发现包含瞬子修正的QCD求和规则在瞬子大小为1/3fm时变得很稳定     

Dual Superconductivity in Abelian Higgs Model of QCD

The study of generalized field associated with Abelian dyons has been undertaken and it has been demonstrated that topologically, a non-Abelian gauge theory is equivalent to a set of Abelian gauge theories supplemented by dyons which undergo condensation leading to confinement and consequently to superconducting model of QCD vacuum, where the Higgs field plays the role of a regulator only. Constructing the effective action for dyonic field in Abelian projection of QCD, it has been demonstrated that any charge (electrical or magnetic) of dyon screens its own direct potential to which it minimally couples and anti-screens the dual potential leading to dual superconductivity in accordance with generalized Meissner effect. In this Abelian projection of QCD an Abelian Higgs model (AHM) has been successfully constructed and it has been shown to incorporate dual superconductivity and confinement as the consequence of dyonic condensation. It has been demonstrated that in AHM t’ Hooft loop creates the string (AHM-string) around which the monopole current under London limit leads to vanishing coherence length in the chromo-magnetic superconductor. It has also been shown that in London limit the squared density of monopole current around AHM-string has a maximum at the distance of the order of penetration length.     

Meson structure in a relativistic many-body approach

Results from an extensive relativistic many-body analysis utilizing a realistic effective QCD Hamiltonian are presented for the meson spectrum. A comparative numerical study of the BCS, Tamm-Dancoff (TDA), and RPA treatments provides new, significant insight into the condensate structure of the vacuum, the chiral symmetry governance of the pion, and the meson spin, orbital, and flavor mass splitting contributions. In contrast to a previous glueball application, substantial quantitative differences are computed between TDA and RPA for the light quark sector with the pion emerging as a Goldstone boson only in the RPA.     

Baryon sum rules and chiral symmetry breaking

In an SVZ-type approach sum rules for baryonic currents have been investigated, without radiative QCD corrections but with the inclusion of non-perturbative terms due to the non-vanishing vacuum expectation value of the quark-antiquark condensate. We give upper bounds for baryon masses, which allow a choice of optimal interpolating operators for low-lying baryon states. The results show that the mentioned vacuum expectation value not only sets the scale for parity splitting but also for the masses of the baryons directly. The alternative way of explicit symmetry breaking by quark masses has also been investigated in the same technical framework.     

QCD Sum Rule External Field Approach and Vacuum Susceptibilities

Based on QCD sum rule three-point and two-point external field formulas respectively, the vector vacuum susceptibilities are calculated at the mean-field level in the framework of the global color symmetry model. It is shown that the above two approaches of determination of the vector vacuum susceptibility may lead to different results. The reason of this contradiction is discussed.     

Tensor Vacuum Susceptibility

Using a nonlocal four-quark condensate in the framework of the modified global colour symmetry model, we determine the tensor vacuum susceptibility needed in the QCD sum rule external field method for the coupling of tensor current to hadron and compare it with the previous estimations.     

Vacuum Condensates and the Anomalous Magnetic Moment of a Dirac Fermion

We address anticipated fermion–antifermion and dimension-4 gauge-field vacuum-condensate contributions to the magnetic portion of the fermion–photon vertex function in the presence of a vacuum with nonperturbative content, such as that of QCD. We discuss how inclusion of such condensate contributions may lead to a vanishing anomalous magnetic moment, in which case vacuum condensates may account for the apparent consistency between constituent quark masses characterizing baryon magnetic moments and those characterizing baryon spectroscopy.     

Vacuum condensates of QCD

We study the properties of QCD vacuum state in this paper. The     

A remark on the large difference between the glueball mass and T<Subscript>c</Subscript> in quenched QCD

The lattice QCD studies indicate that the critical temperature T _c ≃ 260-280 MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass m _G ≃ 1500-1700 MeV, i.e., T _c ≪ m _G. As a consequence of this large difference, the thermal excitation of the glueball in the confinement phase is strongly suppressed by the statistical factor e ^-mG/Tc ≃ 0.00207 even near T ≃ T _c. We consider its physical implication, and argue the abnormal feature of the deconfinement phase transition in quenched QCD from the statistical viewpoint. To appreciate this, we demonstrate a statistical argument of the QCD phase transition using the recent lattice QCD data. From the phenomenological relation between T _c and the glueball mass, the deconfinement transition is found to take place in quenched QCD before a reasonable amount of glueballs is thermally excited. In this way, quenched QCD reveals a question “what is the trigger of the deconfinement phase transition ?” Received: 18 November 2002 / Accepted: 4 February 2003 / Published online: 29 April 2003     

Hadron resonance gas and nonperturbative QCD vacuum at finite temperature

Nonperturbative QCD vacuum with two light quarks at finite temperature was studied in a hadron resonance-gas model. Temperature dependences of the quark and gluon condensates in the confined phase were obtained. It is shown that the quark condensate and one-half (chromoelectric component) of the gluon condensate are evaporated at the same temperature corresponding to the quark-hadron phase transition. With allowance for the temperature shift of hadron masses, the critical temperature was found to be T _c ?190 MeV.     

Lattice results on QCD at high temperature and non-zero baryon number density

Studies of QCD thermodynamics on the lattice now can be performed with an almost realistic quark mass spectrum and on quite large lattices. This will soon allow a controlled extrapolation to the continuum limit. We present recent results on the QCD equation of state, discuss deconfining and chiral symmetry restoring aspects of the QCD transition at vanishing chemical potential and show results on baryon number, electric charge and strangeness fluctuations. We briefly discuss the generic structure of Taylor expansion coefficients in the vicinity of the chiral phase transition and comment on the determination of the anticipated chiral critical point within the framework of Taylor expansions of the QCD partition function.     

A remark on the glueball-gluon coupling

The QCD trace anomaly motivates the consideration of a low energy glueball-gluon coupling . We point out that this should constitute the leading kinetic term for the gluons at low energies. Anti-screening of the gluons by the glueball then induces a classical Coulomb potential of color charges which increases at large distances and motivates the inclusion of a corresponding term in the inter-quark potential. Received: 16 March 1999 / Published online: 20 May 1999