An Introduction to AdS/CFT Correspondence for Phenomenologists

We give a brief introduction to the AdS/CFT correspondence and its application to QCD physics,especiallyits application in the study of quark-gluon-plasma (QGP)formed in the relativistic heavy ion collision (RHIC).Thisreview is based on the talks given in several schools and programs for the phenomenologists working on nuclear physicsand particle physics.

How to Explicitly Calculate Feynman and Wheeler Propagators in the ADS/CFT Correspondence

We discuss, giving all necessary details, the boundary-bulk propagators. We do it for a scalar field, with and without mass, for both the Feynman and the Wheeler cases. Contrary to standard procedure, we do not need here to appeal to any unfounded conjecture (as done by other authors). Emphasize that we do not try to modify standard ADS/CFT procedures, but use them to evaluate the corresponding Feynman and Wheeler propagators. Our present calculations are original in the sense of being the first ones undertaken explicitly using distributions theory (DT). They are carried out in two instances: 1) when the boundary is a Euclidean space and 2) when it is of Minkowskian nature. In this last case we compute also three propagators: Feynman’s, Anti-Feynman’s, and Wheeler’s (half advanced plus half retarded). For an operator corresponding to a scalar field we explicitly obtain, for the first time ever, the two points’ correlations functions in the three instances above mentioned. To repeat, it is not our intention here to improve on ADS/CFT theory but only to employ it for evaluating the corresponding Wheeler’s propagators.

Hua operator on vector bundle: Application to AdS/CFT correspondence of Dirac fields

Hua's theory of harmonic functions on classical domains is generalized to the theory on holomorphic vector bundles over classical domains and further on vector bundles over the real classical domains and quaternion classical domains. In case of the simplest quaternion classical domain there is a relation between Hua operator and Dirac operator,by which an AdS/CFT correspondence of Dirac fields is established.

Static Dielectric Function and Interaction Potential in Strong Coupling with AdS/CFT

In this paper, we study the static dielectric function and interaction potential in strong coupling limit with AdS/CFT correspondence. The dielectric function is depressed compared with that in weak coupling. The interaction potential then presents a weaker screening characteristics in strong coupling, which indicates a smaller Debye mass compared with weak coupling.

Comparing AdS/CFT dipole model to HERA F_2 data

We apply an AdS/CFT-inspired color-dipole model which contains only three free parameters to describe the HERA data for the inclusive structure function F 2 at small Bjorken-x and virtuality.We found that the saturation scale in our AdS/CFT-based parameterization varies in the range of 1 ÷ 3 GeV becoming independent of energy/Bjorken-x at very small x.This leads to the prediction of x-independence of the structure functions at very small x.With the fitted parameters in our model,the predictions for F 2,longitudinal structure function,charm structure function and total photo-production cross-sections in the kinematic regions of future experiments can be given.

Charm structure functions and gluon shadowing effects with the AdS/CFT model

By means of the UGD function extracted from an AdS/CFT inspired saturation model, the charm and bottom structure functions are studied in fixed-order perturbation theory. It is shown that the theoretical results are in good agreement with the recent HERA data. Then, this UGD function is also used to investigate net-kaon rapidity distribution in Au＋Au collisions at RHIC energies and the theoretical results fit well to the BRAHMS data. In the end of this paper, we give the predicted results for nuclear charm structure function at very small x where the popular shadowing parameterizations are invalid.

Surface growth approach for bulk reconstruction in the AdS/BCFT correspondence

In this study,we extend the surface growth approach for bulk reconstruction into the Ad S spacetime with a boundary in the Ad S/BCFT correspondence.We show that the geometry in the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer.Furthermore,we observe that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz(MERA)tensor network.Additionally,we investigate the entanglement of purification within the surface growth process,which not only reveals more refined structure of entanglement entropy in the entanglement wedge but also suggests a selection rule for surface growth in the bulk reconstruction.

Moduli Space of IIB Superstring and SUYM in AdS5 × S^5

This paper consists of two parts. In part I, we interpret the hidden symmetry of the moduli space of lib superstring on AdS5× S^5 in terms of the chiral embedding in AdS5, which turns out to be the CP^3 conformal affine Toda model. We review how the position μ of poles in the Riemann-Hilbert formulation of dressing transformation and the value of loop parameter μ in the vertex operator of affine algebra determine the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU（4） symmetry affinizes the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients μ of twistor. In part Ⅱ by extending the dressing symmetric a.ction of lib string in AdS5×S^5 to the D3 brane, we find a gauged WZW aztion of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structures of left and right a-planes glue into an ambitwistor. The symmetry group of Nahm equations is centrally extended to an affine group, thus we explain why the spectral curve is given by affine Toda.

Holographic Einstein ring of a charged Rastall AdS black hole with bulk electromagnetic field

We study the Einstein images of a charged Rastall AdS black hole(BH)within the fabric of AdS/CFT correspondence.Considering the holographic setup,we analyze the amplitude of the total response function for various values of model parameters.With an increase in parameterλand temperature T,the amplitude of the response function decreases,while it increases with an increase in electric charge e and chemical potentialμ.The influence of frequencyωalso plays an important role in the bulk field,as it is found that decreasingωleads to an increase in the periods of the waves,which means that the amplitude of the response function also depends on the wave source.The relation between T and the inverse of the horizon for various values of parameterλis interpreted under fixed values of other involved parameters.These,in turn,affect the behavior of the response function and the Einstein ring,which may be used to differentiate the present study from previous ones.We construct the holographic images of the BH in bulk via a special optical system.The results show that the Einstein ring always appears with concentric stripes at the position of the north pole,and this ring transforms into a luminosity-deformed ring or bright light spot when the distant observer lies away from the north pole.Finally,we discuss the influence of the associated parameters on the Einstein ring radius,which is consistent with wave optics.

Dynamics of holographic images of scalar-tensor-vector gravity-AdS black holes

Using AdS/CFT correspondence,we analyze the holographic Einstein images via the response function of the complex scalar field as a probe wave on an AdS Schwarzschild scalar-tensor-vector gravity(STVG)black hole(BH).We find that the amplitude of the response function||decreases with increasing values of coupling parameter a and increases with decreasing temperature T.The frequencyωof the wave source also plays a significant role in wave periods;as we increase the values ofω,the periods of waves decrease,indicating that the total response function closely depends on the wave source.Further,we investigate the optical appearance of the holographic images of the BH in bulk.We found that the holographic ring always appears with surrounding concentric stripes when the observer is located at the north pole,and an extremely bright ring appears when the observer is at the position of the photon sphere of the BH.This ring changes into a luminosity-deformed ring or a bright light spot as the observational angle changes.The corresponding brightness profiles show that the luminosity of the ring decreases and the shadow radius increases with increasing values of a.The relation between temperature T and the inverse of the horizonh_e is discussed;T is small at the beginning of the horizon he and then increases as the horizon radius increases.This effect can be used to distinguish the STVG BH solution from other BH solutions.Moreover,these significant features are also reflected in the Einstein ring and corresponding brightness profiles.In addition,we compare the results obtained by wave optics and geometric optics,which align well,implying that the holographic scheme adopted in this study is valid.

Holographic images of an AdS black hole within the framework of f(R) gravity theory

Based on the AdS/CFT correspondence,this study employs an oscillating Gaussian source to numerically study the holographic images of an AdS black hole under f(R)gravity using wave optics.Due to the diffraction of scalar wave,it turns out that one can clearly observed the interference patten of the absolute amplitude of response function on the AdS boundary.Furthermore,it is observed that its peak increases with the f(R)parameterαbut decreases with the global monopoleη,frequencyω,and horizon r_(h).More importantly,the results reveal that the holographic Einstein ring is a series of concentric striped patterns for an observer at the North Pole and that their center is analogous to a Poisson-Arago spot.This ring can evolve into a luminosity-deformed ring or two light spots when the observer is at a different position.According to geometrical optics,it is true that the size of the brightest holographic ring is approximately equal to that of the photon sphere,and the two light spots correspond to clockwise and anticlockwise light rays.In addition,holographic images for different values of black holes and optical system parameters were obtained,and different features emerged.Finally,we conclude that the holographic rings of the AdS black hole in modified gravities are more suitable and helpful for testing the existence of a gravity dual for a given material.

量子纠缠与时空结构

众所周知,自然界中存在着四种基本相互作用,分别为强相互作用、弱相互作用、电磁相互作用与引力相互作用。然而,前三者可以在量子力学的框架下自洽,只有特殊的引力相互作用尚未与其他相互作用统一。因此,追求引力的量子化是现代物理学最迫切和首要的目标。物理学家们发现,可以利用量子场论的方法来研究引力理论。在这过程中,我们发现量子纠缠、几何以及时空定域性之间的关系,这似乎暗示了通往量子引力的研究方向。通过量子纠缠,我们希望进一步探索量子引力领域,为引力的量子化找到一个突破口,从而发现时空的本质。文章简要回顾量子纠缠熵的历史发展,并讨论纠缠熵与几何之间的关系。

五维Gauss-Bonnet纯时空下全息纠缠熵解析约束方程

引力/规范场论对偶作为研究黑洞以及量子引力性质的一种有力工具,其各种修正模式也得到越来越多的研究.Gauss-Bonnet修正描述了量子或者弦效应对时空本身的高阶曲率修正,对理解量子引力具有重要作用.由于其度规的复杂性,研究Gauss-Bonnet时空与规范场论对偶时,一般采用数值计算的方法得到全息纠缠熵的一些性质,利用反德西特时空/共形场论(AdS/CFT)对偶理论推导了五维Gauss-Bonnet纯时空下全息纠缠熵所对应的极值面应该满足的解析约束方程,为更进一步推导Gauss-Bonnet黑洞时空下全息纠缠熵的解析演化提供了新的基础.

掺杂全息费米系统

构建了包括两个规范场和一个中性标量场的两流体模型.数值得到渐近标量毛AdS黑膜解.模型导入了两个可调节的化学势,从而导入了可控的掺杂参数.研究了特定参数下全息费米系统的性质.研究表明随着赝标量汤川秀树耦合增大,能隙打开,标志着系统衍生出绝缘相.固定赝标量汤川秀树耦合,随着掺杂参数的增大,能隙打开的临界值减少,能隙的形成更容易.并给出了相应的温度-掺杂相图.最后,根据模型参数,将模型分类.

一类新的Stückelberg全息超导模型

本文研究了含Stückelberg机理的黑洞全息超导模型.通过选取标量场新的高阶修正形式,建立了新的Stückelberg黑洞全息超导模型.通过研究模型参数对标量场凝聚的影响,发现了当模型参数大于临界值时,高阶修正可以引起一阶相变.同时本文还考查了反作用对临界值的影响.

带有高阶修正的全息p波超导体相变

在探子极限下,通过数值方法研究了高阶修正对超导体相变的影响。具体来说,把带质量的麦克斯韦复矢量场和Weyl张量平方修正项耦合到4维AdS黑洞中构造了带有高阶修正的p波超导体模型。结果表明在比较宽的高阶参数范围内仍然可以得到比较合理的超导凝聚行为。在最低朗道能级,磁场可以诱导超导相变,且高阶修正抑制相变。然而,在激发态能级,磁场破坏超导相变,且高阶修正促进相变。

4阶导数修正全息超导体

构建了一个4阶导数引力框架下的全息超导体模型.主要研究了凝聚态形成,临界温度T_c及超导能隙ω_g/T_c的变化规律.研究结果表明,高斯-博内(Gauss-Bonnet,GB)耦合阻碍凝聚的形成,促使超导能隙变大;而外尔耦合项可以使得超导能隙从接近BCS理论的ω_g/T_c≈3.5到大于标准全息超导的ω_g/T_c≈8变化.4阶导数引力框架下的全息超导体模型给出了更丰富的物理图像,有助于研究全息对偶系统.

Holographic p-Wave Superconductors in Quintessence AdS Black Hole Spacetime

We construct a holographic p-wave superconductor model in the background of quintessence AdS black hole with an SU（2） Yang-Mills gauge field and then probe the effects of quintessence on the holographic p-wave superconduc- tor. We investigate the relation between the critical temperature and the state parameter of quintessence, and present the numerical results for electric conductivity. It is shown that the condensation of the vector field becomes harder as the absolute value of the state parameter increases. Unlike the scalar condensate in the s-wave model, the condensation of the vector field in p-wave model can occur in the total value range of the state parameter wq of quintessence. These results could help us know more about holographic superconductor and dark energy.

Thermal Phase in Bubbling Geometries

We use matrix model to study thermal phase in bubbling half-BPS type liB geometries with SO（4） × SO（4） symmetry. Near the horizon limit, we find that thermal vacua of bubbling geometries have disjoint parts, and each part is one kind of phase of the thermal system. We connect the thermal dynamics of bubbling geometries with one-dimensional fermions thermal system. Finally, we try to give a new possible way to resolve information loss puzzle.

Holographic Schwinger effect in a soft wall AdS/QCD model

We perform a potential analysis for the holographic Schwinger effect in a deformed AdS5 model with conformal invariance broken by a background dilaton.We evaluated the static potential by analyzing the classical action of a string attached to a rectangular Wilson loop on a probe D3 brane located at an intermediate position in the bulk AdS space.We observed that the inclusion of the chemical potential tends to enhance the production rate,which is opposite to the effect of the confining scale.In addition,we calculated the critical electric field based on the Dirac-Born-Infeld(DBI)action.