arXiv subjects

Danning Li

Publications and source records attributed to Danning Li.

71 records · Page 4Linked to original sources

arXiv2016

Dynamical corrections to the anomalous holographic softwall model: the pomeron and the odderon

In this work we use the holographic softwall AdS/QCD model with anomalous dimension contributions coming from two different QCD beta functions to calculate the masses of higher spin glueball states for both even and odd spins and its respective Regge trajectories, related to the pomeron and the odderon, respectively. We further investigate this model taking into account dynamical corrections due to a dilaton potential consistent with Einstein equations in 5 dimensions. The results found in this work for the Regge trajectories within the anomalous softwall model with dynamical corrections are consistent with those presented in the literature.

hep-ph↗

arXiv2016

SURE Information Criteria for Large Covariance Matrix Estimation and Their Asymptotic Properties

Consider $n$ independent and identically distributed $p$-dimensional Gaussian random vectors with covariance matrix $Σ.$ The problem of estimating $Σ$ when $p$ is much larger than $n$ has received a lot of attention in recent years. Yet little is known about the information criterion for covariance matrix estimation. How to properly define such a criterion and what are the statistical properties? We attempt to answer these questions in the present paper by focusing on the estimation of bandable covariance matrices when $p>n$ but $\log(p)=o(n)$. Motivated by the deep connection between Stein's unbiased risk estimation (SURE) and AIC in regression models, we propose a family of generalized SURE ($\text{SURE}_c$) indexed by $c$ for covariance matrix estimation, where $c$ is some constant. When $c$ is 2, $\text{SURE}_2$ provides an unbiased estimator of the Frobenious risk of the covariance matrix estimator. Furthermore, we show that by minimizing $\text{SURE}_2$ over all possible banding covariance matrix estimators we attain the minimax optimal rate of convergence and the resulting estimator behaves like the covariance matrix estimator obtained by the so-called oracle tuning. On the other hand, we also show that $\text{SURE}_2$ is selection inconsistent when the true covariance matrix is exactly banded. To fix the selection inconsistency, we consider using SURE with $c=\log(n)$ and prove that by minimizing $\text{SURE}_{\log(n)}$ we select the true bandwith with probability tending to one. Therefore, our analysis indicates that $\text{SURE}_2$ and $\text{SURE}_{\log(n)}$ can be regarded as the AIC and BIC for large covariance matrix estimation, respectively.

math.ST↗

arXiv2015

Joint limiting laws for high-dimensional independence tests

Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However, quadratic form statistics suffer from low power against sparse alternatives, and extreme-value form statistics suffer from low power against dense alternatives with small disturbances and may have size distortions due to its slow convergence. For real-world applications, it is important to derive powerful testing procedures against more general alternatives. Based on intermediate limiting distributions, we derive (model-free) joint limiting laws of extreme-value form and quadratic form statistics, and surprisingly, we prove that they are asymptotically independent. Given such asymptotic independencies, we propose (model-free) testing procedures to boost the power against general alternatives and also retain the correct asymptotic size. Under the high-dimensional setting, we derive the closed-form limiting null distributions, and obtain their explicit rates of uniform convergence. We prove their consistent statistical powers against general alternatives. We demonstrate the performance of our proposed test statistics in simulation studies. Our work provides very helpful insights to high-dimensional independence tests, and fills an important gap.

math.ST↗

arXiv2015

Chiral Phase Transition in the Soft-Wall Model of AdS/QCD

We investigate the chiral phase transition in the soft-wall model of AdS/QCD at zero chemical potential for two-flavor and three-flavor cases, respectively. We show that there is no spontaneous chiral symmetry breaking in the original soft-wall model. After detailed analysis, we find that in order to realize chiral symmetry breaking and restoration, both profiles for the scalar potential and the dilaton field are essential. The scalar potential determines the possible solution structure of the chiral condensate, except the mass term, it takes another quartic term for the two-flavor case, and for the three-flavor case, one has to take into account an extra cubic term due to the t'Hooft determinant interaction. The profile of the dilaton field reflects the gluodynamics, which is negative at a certain ultraviolet scale and approaches positive quadratic behavior at far infrared region. With this set-up, the spontaneous chiral symmetry breaking in the vacuum and its restoration at finite temperature can be realized perfectly. In the two-flavor case, it gives a second order chiral phase transition in the chiral limit, while the transition turns to be a crossover for any finite quark mass. In the case of three-flavor, the phase transition becomes a first order one in the chiral limit, while above sufficient large quark mass it turns to be a crossover again. This scenario agrees exactly with the current understanding on chiral phase transition from lattice QCD and other effective model studies.

hep-ph↗

arXiv2015

Chiral and Deconfining Phase Transitions from Holographic QCD Study

A first attempt to accommodate the chiral and deconfining phase transitions of QCD in the bottom-up holographic framework is given. We constrain the relation between dilaton field $ϕ$ and metric warp factor $A_e$ and get several reasonable models in the Einstein-Dilaton system. Using the potential reconstruction approach, we solve the corresponding gravity background. Then we fit the background-related parameters by comparing the equation of state with the two-flavor lattice QCD results. After that we study the temperature dependent behavior of Polyakov loop and chiral condensate under those background solutions. We find that the results are in good agreement with the two-flavor lattice results. All the studies about the equation of state, the Polyakov loop and the chiral condensate signal crossover behavior of the phase transitions, which is consistent with the current understanding on the QCD phase transitions with physical quark mass. Furthermore, the extracted transition temperatures are comparable with the two-flavor lattice QCD results.

hep-ph↗

arXiv2015

Realization of chiral symmetry breaking and restoration in holographic QCD

With proper profiles of the scalar potential and the dilaton field, for the first time, the spontaneous chiral symmetry breaking in the vacuum and its restoration at finite temperature are correctly realized in the holographic QCD framework. In the chiral limit, a nonzero chiral condensate develops in the vacuum and decreases with temperature, and the phase transition is of 2nd order for two-flavor case and of 1st order for three-flavor case. In the case of explicit chiral symmetry breaking, in two-flavor case, the 2nd order phase transition turns to crossover with any nonzero current quark mass, and in three-flavor case, the 1st order phase transition turns to crossover at a finite current quark mass. The correct description of chiral symmetry breaking and restoration makes the holographic QCD models more powerful in dealing with non-perturbative QCD phenomena. This framework can be regarded as a general set up in application of AdS/CFT to describe conventional Ginzburg-Landau-Wilson type phase transitions, e.g. in condensed matter and cosmology systems.

hep-ph↗

arXiv2014

Temperature dependent transport coefficients in a dynamical holographic QCD model

We investigate temperature dependent behavior of various transport coefficients in a dynamical holographical QCD model. We show the nontrivial temperature dependent behavior of the transport coefficients, like bulk viscosity, electric conductivity as well as jet quenching parameter, and it is found that all these quantities reveal information of the phase transition. Furthermore, with introducing higher derivative corrections in 5D gravity, the shear viscosity over entropy density ratio also shows a valley around phase transition, and it is found that the shear viscosity over entropy density ratio times the jet quenching over temperature cubic ratio almost remains as a constant above phase transition, and the value is two times larger than the perturbative result in Phys.Rev.Lett.99.192301(2007).

hep-ph↗

arXiv2014

Dynamical holographic QCD model

We develop a dynamical holographic QCD model, which resembles the renormalization group from ultraviolet (UV) to infrared (IR). The dynamical holographic model is constructed in the graviton-dilaton-scalar framework with the dilaton background field $Φ$ and scalar field $X$ responsible for the gluodynamics and chiral dynamics, respectively. We summarize our results on hadron spectra, QCD phase transition and transport properties including the jet quenching parameter and the shear/bulk viscosity in the framework of the dynamical holographic QCD model.

hep-ph↗

arXiv2014

Enhancement of jet quenching around phase transition: result from the dynamical holographic model

The phase transition and jet quenching parameter ${\hat q}$ have been investigated in the framework of dynamical holographic QCD model. It is found that both the trace anomaly and the ratio of the jet quenching parameter over cubic temperature ${\hat q}/T^3$ show a peak around the critical temperature $T_c$, and the ratio of jet quenching parameter over entropy density ${\hat q}/s$ sharply rises at $T_c$. This indicates that the jet quenching parameter can characterize the phase transition. The effect of jet quenching parameter enhancement around phase transition on nuclear modification factor $R_{AA}$ and elliptic flow $v_2$ have also been analyzed, and it is found that the temperature dependent jet quenching parameter from dynamical holographic QCD model can considerably improve the description of jet quenching azimuthal anisotropy as compared with the conformal case.

hep-ph↗

arXiv2013

Dynamical holographic QCD model: resembling renormalization group from ultraviolet to infrared

Resembling the renormalization group from ultraviolet to infrared, we construct a dynamical holographic model in the graviton-dilaton-scalar framework, where the dilaton background field $Φ$ and scalar field $X$ are responsible for the gluodynamics and chiral dynamics, respectively. At the UV boundary, the dilaton field is dual to the dimension-4 gluon operator, and the scalar field is dual to the dimension-3 quark-antiquark operator. The metric structure at IR is automatically deformed by the nonperturbative gluon condensation and chiral condensation in the vacuum. The produced scalar glueball spectra in the graviton-dilaton framework agree well with lattice data, and the light-flavor meson spectra generated in the graviton-dilaton-scalar framework are in well agreement with experimental data. Both the chiral symmetry breaking and linear confinement are realized in this dynamical holographic QCD model. The necessary condition for the existence of linear quark potential is discussed, and the pion form factor is also investigated in the dynamical holographic QCD model.

hep-ph↗

arXiv2013

Dynamical holographic QCD model for glueball and light meson spectra

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 on the gluodynamical background. For two forms of dilaton background field $Φ=μ_G^2z^2$ and $Φ=μ_G^2z^2\tanh(μ_{G^2}^4z^2/μ_G^2)$, the quadratic correction to dilaton background field at infrared encodes important non-perturbative gluodynamics and naturally induces a deformed warp factor of the metric. By self-consistently solving the 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.

hep-ph↗

arXiv2013

Entanglement Temperature in Non-conformal Cases

Potential reconstruction can be used to find various analytical asymptotical AdS solutions in Einstein dilation system generally. We have generated two simple solutions without physical singularity called zero temperature solutions. We also proposed a numerical way to obtain black hole solution in Einstein dilaton system with special dilaton potential. By using this method, we obtain the corresponding black hole solutions numerically and investigate the thermal stability of the black hole by comparing the free energy of thermal gas and the corresponding black hole. In two groups of non-conformal gravity solutions obtained in this paper, we find that the two thermal gas solutions are more unstable than black hole solutions respectively. Finally, we consider black hole solutions as a thermal state of zero temperature solutions to check that the first thermal dynamical law exists in entanglement system from holographic point of view.

hep-th↗

arXiv2013

Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations

We investigate the random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n,p). In the case that the sample size n is much smaller than the dimension of the population distribution p, a common situation in modern data, we approximate the beta-Laguerre ensemble by a beta-Hermite ensemble which is a generalization of the real, complex and quaternion Wigner matrices. As corollaries, when n is much smaller than p, we show that the largest and smallest eigenvalues of the complex Wishart matrix are asymptotically independent; we obtain the limiting distribution of the condition numbers as a sum of two i.i.d. random variables with a Tracy-Widom distribution, which is much different from the exact square case that n=p by Edelman (1988); we propose a test procedure for a spherical hypothesis test. By the same approximation tool, we obtain the asymptotic distribution of the smallest eigenvalue of the beta-Laguerre ensemble. In the second part of the paper, under the assumption that n is much smaller than p in a certain scale, we prove the large deviation principles for three basic statistics: the largest eigenvalue, the smallest eigenvalue and the empirical distribution of eigenvalues, where the last large deviation is derived by using a non-standard method.

math.PR↗

arXiv2012

Accommodate chiral symmetry breaking and linear confinement in a dynamical holographic QCD model

We construct a self-consistent holographic QCD model which can realize two most important phenomena of QCD, i.e. chiral symmetry breaking and confinement. The model is formulated in the framework of graviton-dilaton-scalar system, where the dilaton field is of dimension-2 which might be 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. Within this framework, both Regge spectra of hadrons and the linear potential between quarks can be accommodated. It is also found that the negative dilaton background can be safely excluded in this framework.

hep-ph↗

arXiv2012

A dynamical holographic QCD model for chiral symmetry breaking and linear confinement

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.

hep-th↗

arXiv2012

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

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 $T-μ$ plane is in quite good agreement with the one from recent lattice results and effective models of QCD.

hep-th↗

arXiv2011

Thermodynamics of deformed AdS$_5$ model with a positive/negative quadratic correction in graviton-dilaton system

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 framwork, we solve the black-hole background, the corresponding dilaon field and the dilaton potential for the deformed AdS$_5$ model with a positive/negative quadratic correction. We systematically investigate the thermodynamical properties of the deformed AdS$_5$ 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 ${\rm AdS}_5$.

hep-th↗