The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling $$\alpha_s^{AdS}(Q^2)$$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $$ \sim 1$$ GeV. The resulting $$\beta$$-function appears to capture the essential characteristics of the full $$\beta$$-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on $$\alpha_s^{AdS}(Q^2)$$.

Nonperturbative QCD coupling and its β function from light-front holography

We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n, J, L, S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field. We show that in the case of the bound-state problem (hadronic mass spectrum) two versions of the model with a positive and negative dilaton profile are equivalent to each other by a special transformation of the bulk field. We also comment on recent works which discuss the dilaton sign in the context of soft-wall approaches.

Dilaton in a soft-wall holographic approach to mesons and baryons

By solving the Einstein equations of the graviton coupling with a real scalar dilaton field, we establish a general framework to self-consistently solve the geometric background with black-hole for any given phenomenological holographic models. In this framework, we solve the black-hole background, the corresponding dilaon field and the dilaton potential for the deformed AdS5 model with a positive/negative quadratic correction. We systematically investigate the thermodynamical properties of the deformed AdS5 model with a positive and negative quadratic correction, respectively, and compare with lattice QCD on the results of the equation of state, the heavy quark potential, the Polyakov loop and the spatial Wilson loop. We find that the bulk thermodynamical properties are not sensitive to the sign of the quadratic correction, and the results of both deformed holographic QCD models agree well with lattice QCD result for pure SU(3) gauge theory. However, the results from loop operators favor a positive quadratic correction, which agree well with lattice QCD result. Especially, the result from the Polyakov loop excludes the model with a negative quadratic correction in the warp factor of AdS5.

Thermodynamics of deformed AdS 5 model with a positive/negative quadratic correction in graviton-dilaton system

In this work, we offer a dynamical soft-wall model to describe the gluodynamics and chiral dynamics in one systematical framework. We firstly construct a quenched dynamical holographic QCD (hQCD) model in the graviton-dilaton framework for the pure gluon system, then develop a dynamical hQCD model for the two flavor system in the graviton-dilaton-scalar framework by adding light flavors 011 the gluodynamical background. For two forms of dilaton background field Phi = mu(2z2)(G) and Phi = mu(2z2)(G) tanh(mu(42z2)(G)/mu(2)(G)), the quadratic correction to dilaton background field at infrarcd encodes important non-pert urbative gluodynamics and naturally induces a deformed warp factor of the metric. By self-consistently solving Hie deformed metric induced by the dilaton background field, we find that the scalar glueball spectra in the quenched dynamical model is in very well agreement with lattice data. For two flavor system in the graviton-dilaton-scalar framework, the deformed metric is self-consistently solved by considering both the chiral condensate and nonperturbative gluodynamics in the vacuum, which are responsible for the chiral symmetry breaking and linear confinement, respectively. It is found that the mixing between the chiral condensate and gluon condensate is important to produce the correct light flavor meson spectra. The pion form factor and the vector couplings are also investigated in the dynamical hQCD model. Besides, we give the criteria for the existence of linear quark potential from the metric structure, and show a negative quadratic dilaton background field is not favored in the graviton-dilaton framework.

Dynamical holographic QCD model for glueball and light meson spectra

By use of the potential reconstruction approach we obtain a series of asymptotically AdS (aAdS) black hole solutions in an Einstein-Maxwell-Dilaton (EMD) system. Basing on the solutions of the system, we reconstruct a semi-analytical holographic QCD (hQCD) model with a quadratic term in warped factor. We discuss some aspects of the hQCD model, in particular we calculate the free energy of two static color sources (a heavy quark-antiquark pair) which is an important order parameter to describe confinement/deconfinement phase transition. The behavior of the free energy with respect to temperature and chemical potential is studied. We find that in the hQCD model the deconfinement phase transition can be realized and a critical point occurs. The resulting phase diagram in the temperature-chemical potential T-mu plane is in quite good agreement with the one from recent lattice results and effective models of QCD.

A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system

I propose to change the sign of the dilaton in the infrared (IR) soft-wall anti-de Sitter/QCD model, in order to implement confinement. The deformed model exhibits interesting properties, especially in describing chiral symmetry breaking. The expectation value of the scalar field X, which determines the quark mass and condensate, approaches a constant in the IR limit, rather than blows up in the original model. In contrast to the estimate in [M. Shifman and A. Vainshtein, Phys. Rev. D 77, 034002 (2008).], this kind of solution will not lead to chiral symmetry restoration for highly-excited states due to the property of the harmonic-oscillator equation. Instead, it will guarantee the Regge behavior of the axial meson spectrum and also the pseudoscalar mesons. The value of the condensate can be fixed by requiring that the pion be massless in the chiral limit, but only under some approximation in the present model. We also find that, by relaxing the IR boundary conditions, the unphysical massless state in the vector channel can be eliminated.

Fen Zuo

Papers

Improved soft-wall model with a negative dilaton