Koji Hashimoto, Yoshinori Matsuo
Saturation of the nuclear binding energy is one of the most important properties of atomic nuclei. We derive the saturation in holographic QCD, by building a shell-model-like mean-field nuclear potential from the nuclear density profile obtained in a holographic multi-baryon effective theory. The numerically estimated binding energy is close to the experimental value.
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We present a recent proposal of a simple prescription for including low-energy weak-interactions into the framework of holographic QCD, based on the standard AdS/CFT dictionary of double-trace deformations. This opens a new perspective on phenomenological applications of holographic QCD: calculating weak observables in the strongly coupled regime of QCD. The idea is general enough to be implemented in any holographic model. Its efficiency and usefulness are demonstrated by performing few exemplar calculations of weak reactions involving mesons and baryons, within the Sakai-Sugimoto and hard/so…
We study nuclear symmetry energy of dense matter using holographic QCD. We calculate it in a various holographic QCD models and show that the scaling index of the symmetry energy in dense medium is almost invariant under the smooth deformation of the metric as well as the embedding shape of the probe brane. We find that the scaling index depends only on the dimensionality of the branes and space-time. Therefore the scaling index of the symmetry energy characterizes the universality classes of holographic QCD models. We suggest that the scaling index might be also related to the non-fermi liqui…
At the dawn of a new theoretical tool based on the AdS/CFT correspondence for nonperturbative aspects of quantum chromodynamics, we give an interim review on the new tool, holographic QCD, with some of its accomplishment. We try to give an A-to-Z picture of the holographic QCD, from string theory to a few selected top-down holographic QCD models with one or two physical applications in each model. We may not attempt to collect diverse results from various holographic QCD model studies.
In the large 't Hooft coupling limit, the hadronic size of baryon is small and nucleon-nucleon potential is obtained from massless pseudo-scalar exchanges and an infinite tower of spin one mesons exchanges. In this paper we use the holographic nucleon-nucleon interaction and obtain the corresponding potential and binding energy for deuteron and tritium nuclei. The obtained potentials are repulsive at short distances and clearly become zero by increasing distance as we expected.
We provide a calculation of N-body (N>2) nucleon interactions at short distances in holographic QCD. In the Sakai-Sugimoto model of large N_c massless QCD, N baryons are described by N Yang-Mills instantons in 5 spacetime dimensions. We compute a classical short distance interaction hamiltonian for N 'tHooft instantons. This corresponds to N baryons sharing identical classical spins and isospins. We find that genuine N-body nuclear forces turn out to vanish for N>2, at the leading order. This suggests that classical N-body forces are always suppressed compared with 2-body forces.
We provide, for non-experts, a brief overview of holographic QCD and a review of a recent proposal of matrix-description of multi-baryon systems in holographic QCD. Based on the matrix model, we derive the baryon interaction at short distances in multi-flavor holographic QCD. We show that there is a very universal repulsive core of inter-baryon forces for generic number of flavors. This is consistent with a recent lattice QCD analysis for N_f = 2, 3 where repulsive core looks universal. We also provide a comparison of our results with the lattice QCD and the operator product expansion (OPE) an…
We show that the Aharonov-Bohm effect in the nuclear matrix model derives the statistical nature of nucleons in holographic QCD. For N_c= odd (even), the nucleon is shown to be a fermion (boson).
We further analyze the holographic dipole-dipole scattering amplitude developed in arXiv:1202.0831, 1205.3223. Gribov diffusion at strong coupling yields the scattering amplitude in a confining background. We compare the holographic result for the differential cross section to proton-proton and deeply virtual Compton scattering data.
We review 5D holographic approaches to finite temperature QCD. Thermodynamic properties of the "hard-wall" and the "soft-wall" models are derived. Various non-realistic features in these models are cured by the set-up of improved holographic QCD, that we review here.
We propose a simple prescription for including low-energy weak-interactions into the framework of holographic QCD, based on the standard AdS/CFT dictionary of double-trace deformations. As our proposal enables us to calculate various electro-weak observables involving strongly coupled QCD, it opens a new perspective on phenomenological applications of holographic QCD. We illustrate efficiency and usefulness of our method by performing a few exemplar calculations; neutron beta decay, charged pion weak decay, and meson-nucleon parity non-conserving (PNC) couplings. The idea is general enough to …
We study baryons in holographic QCD with $D4/D8/\bar{D8}$ multi $D$ brane system. In holographic QCD, the baryon appears as a topologically non-trivial chiral soliton in a four-dimensional effective theory of mesons, which is called `Brane-induced Skyrmion'. We derive and calculate the Euler-Lagrange equation for the hedgehog configuration with chiral profile $F(r)$ and $ρ$-meson profile $\tilde G(r)$, and obtain the soliton solution of the holographic QCD.
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.
We study the nuclear symmetry energy of dense matter using holographic QCD. To this end, we consider two flavor branes with equal quark masses in a D4/D6/D6 model. We find that at all densities the symmetry energy monotonically increases. At small densities, it exhibits a power law behavior with the density, $E_{\rm sym} \sim ρ^{1/2}$.
To realize massive pions, we study variations of the holographic model of massless QCD using the D4/D8/anti-D8 brane configuration proposed by Sakai and Sugimoto. We propose deformations which break the chiral symmetry explicitly and compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. We also argue a chiral perturbation corresponding to our deformation.
We study baryons and baryonic matter in holographic QCD with $D4/D8/\bar{D8}$ multi-$D$ brane system. In large-$N_c$ holographic QCD, the baryon appears as a topologically non-trivial chiral soliton, which is called ``brane-induced Skyrmion''. We also analyze the features of the baryonic matter in holographic QCD by investigating the system of single brane-induced Skyrmion on a three-dimensional closed manifold $S^3$. We propose a new interesting picture of ``pion dominance'' near the critical density.
Using holographic QCD based on D4-branes and D8-anti-D8-branes, we have computed couplings of glueballs to light mesons. We describe glueball decay by explicitly calculating its decay widths and branching ratios. Interestingly, while glueballs remain less well understood both theoretically and experimentally, our results are found to be consistent with the experimental data for the scalar glueball candidate f_0(1500). More generally, holographic QCD predicts that decay of any glueball to 4 $π_0$ is surpressed, and that mixing of the lightest glueball with $q\bar{q}$ mesons is small.
We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such Q…
The aim of these lectures is to convey a working knowledge of Light Front Holographic QCD and Supersymmetric Light Front Holographic QCD. We first give an overview of holographic QCD in general and then concentrate on the application of the holographic methods on QCD quantized in the light front form. We show how the implementation of the supersymmetric algebra fixes the interaction and how one can obtain hadron mass spectra with the minimal number of parameters. We also treat propagators and compare the holographic approach with other non-perturbative methods. In the last chapter we describe …
We propose a five-dimensional framework for modeling low-energy properties of QCD. In the simplest three parameter model we compute masses, decay rates and couplings of the lightest mesons. The model fits experimental data to within 10%. The framework is a holographic version of the QCD sum rules, motivated by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. The model naturally incorporates properties of QCD dictated by chiral symmetry, which we demonstrate by deriving the Gell-Mann-Oakes-Renner relationship for the pion mass.
We introduce the 5-dimension dynamical holographic QCD model, which is constructed in the graviton-dilaton-scalar framework with the dilaton background field $Φ$ and the scalar field $X$ responsible for the gluodynamics and chiral dynamics, respectively. We review our results on the hadron spectra including the glueball and light meson spectra, QCD phase transitions and transport properties in the framework of the dynamical holographic QCD model.
We describe the temperature-chemical potential phase diagrams of holographic models of a range of strongly coupled gauge theories that display chiral symmetry breaking/restoration transitions. The models are based on the D3/probe-D7 system but with a phenomenologically chosen running coupling/dilaton profile. We realize chiral phase transitions with either temperature or density that are first or second order by changing the dilaton profile. Although the models are only caricatures of QCD they show that holographic models can capture many aspects of the QCD phase diagram and hint at the depend…
We calculate the low energy constants of four-nucleon interactions in an effective chiral Lagrangian in holographic QCD. We start with a D4-D8 model to obtain meson-nucleon interactions and then integrate out massive mesons to obtain the four-nucleon interactions in 4D. We end up with two low energy constants at the leading order and seven of them at the next leading order, which is consistent with the effective chiral Lagrangian. The values of the low energy constants are evaluated with the first five Kaluza-Klein resonances.
We present a holographic realization of large Nc massless QCD in two dimensions using a D2/D8 brane construction. The flavor axial anomaly is dual to a three dimensional Chern-Simons term which turns out to be of leading order, and it affects the meson spectrum and holographic renormalization in crucial ways. The massless flavor bosons that exist in the spectrum are found to decouple from the heavier mesons, in agreement with the general lore of non-Abelian bosonization. We also show that an external dynamical photon acquires a mass through the three dimensional Chern-Simons term as expected f…
We study the dependence of the chiral condensate on external magnetic field in the context of holographic QCD at large number of flavors. We consider a holographic QCD model where the flavor degrees of freedom fully backreact on the color dynamics. Perturbative QCD calculations have shown that $B$ acts constructively on the chiral condensate, a phenomenon called "magnetic catalysis". In contrast, recent lattice calculations show that, depending on the number of flavors and temperature, the magnetic field may also act destructively, which is called "inverse magnetic catalysis". Here we show tha…
We study the H-dibaryon (uuddss) in holographic QCD for the first time. Holographic QCD is derived from a QCD-equivalent D-brane system ($S^1$-compactified D4/D8/$\overline{\rm D8}$) in the superstring theory via the gauge/gravity correspondence. In holographic QCD, all baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons. In this framework, the H-dibaryon can be described as an SO(3)-type hedgehog state. We present the formalism of the H-dibaryon in holographic QCD, and perform the calculation to investigate its properties in the chiral limit.
We study baryons and baryonic matter in holographic QCD using a D4/D8/$\bar{\rm D8}$ multi-D-brane system in the superstring theory. We obtain the chiral soliton solution for baryons in the four-dimensional meson theory derived from the multi-D-brane system. For the analysis of finite baryon-density matter, we investigate the chiral soliton on $S^3$ in holographic QCD, and find the delocalization of the soliton, i.e., the swelling of baryons in dense matter.
We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. The kinetic gauge function can be fixed by requesting the linear Regge spectrum of mesons. We calculate the free energy to obtain the phase diagram of the holographic QCD model.
Based on the chiral perturbation theory (ChPT) with the hidden local symmetry, we propose a methodology to calculate the large $N_c$ corrections in the holographic QCD (HQCD). As an example, we apply the method to an HQCD model recently proposed by Sakai and Sugimoto. We show that the $ρ$-$π$-$π$ coupling becomes in good agreement with the experiment due to the $1/N_c$-subleading corrections.
In this paper, we calculate analytically the baryonic density and susceptibilities, which are sensitive probes to the fermionic degrees of freedom, in a holographic model of QCD both in its hot QGP phase and in its cold dense phase. Interesting patterns due to strong coupling dynamics will be shown and valuable lessons for QCD will be discussed.
We review the description of deep inelastic scattering using some AdS/QCD phenomenological models.
We obtain the gluon parton distribution functions (PDFs) in the proton within the extended light-front holographic QCD framework, where the proton couples with the spin-two Pomeron in Anti-de Sitter space, together with constraints imposed by the Veneziano model. The gluon helicity asymmetry, after satisfying the perturbative QCD constraints at small and large longitudinal momentum regions, agrees with existing experimental measurements. The polarized gluon distribution is consistent with global analyses. We predict the gluon helicity contribution to the proton spin, $ΔG=0.221^{+0.056}_{-0.044…
We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the QCD lattice data of the chiral condensate as a function of the quark mass. This establishes a data-driven holographic modeling of QCD -- machine learning holographic QCD. The modeling consists of two steps for solving inverse problems. The first inverse problem is to find the emergent bulk geometry consistent with the lattice QCD simulation data at the boundary. We solve this problem with the refinement of neural ordinary differential equation, a machine learning technique. The second inverse probl…
We consider a bottom-up holographic model of QCD at finite temperature T and magnetic field B, and study dependence of thermodynamics and CP-odd transport on these variables. As the magnetic field couples to the flavor sector only, one should take the Veneziano limit where the number of flavors and colors are large while their ratio is kept fixed. We investigate the corresponding holographic background in the approximation where the ratio of flavors to colors is finite but small. We demonstrate that B-dependence of the entropy of QCD is in qualitative agreement with the recent lattice studies.…
In a simple holographic model for QCD in which the Chern-Simons term is incorporated to take into account the QCD chiral anomaly, we show that baryons arise as stable solitons which are the 5D analogs of 4D skyrmions. Contrary to 4D skyrmions and previously considered holographic scenarios, these solitons have sizes larger than the inverse cut-off of the model, and therefore they are predictable within our effective field theory approach. We perform a numerical determination of several static properties of the nucleons and find a satisfactory agreement with data. We also calculate the amplitud…
The light-front holographic QCD approach is used to describe baryon spectroscopy and the systematics of nucleon transition form factors.
We discuss a derivation of the quadratic in fields part of action of bottom-up holographic models from some general properties of the large-Nc limit in QCD.
We study the effect of magnetic field $B$ on the critical temperature $T_{c}$ of the confinement-deconfinement phase transition in hard-wall AdS/QCD, and holographic duals of flavored and unflavored $\mathcal{N}=4$ super-Yang Mills theories on $\mathbb{R}^3\times \rm S^1$. For all of the holographic models, we find that $T_{c}(B)$ decreases with increasing magnetic field $B\ll T^2$, consistent with the inverse magnetic catalysis recently observed in lattice QCD for $B\lesssim 1~GeV^2$. We also predict that, for large magnetic field $B\gg T^2$, the critical temperature $T_{c}(B)$, eventually, s…
We study the physics with finite nuclear density in the framework of AdS/QCD with holographic baryon field included. Based on a mean field type approach, we introduce the nucleon density as a bi-fermion condensate of the lowest mode of the baryon field and calculate the density dependence of the chiral condensate and the nucleon mass. We observe that the chiral condensate as well as the mass of nucleon decrease with increasing nuclear density. We also consider the mass splitting of charged vector mesons in iso-spin asymmetric nuclear matter.
The paper discusses phenomena close to the critical QCD temperature, using the holographic model. One issue studied is the overcooled high-T phase, in which we calculate quasi normal sound modes. We do not find instabilities associated with other first order phase transitions, but nevertheless observe drastic changes in sound propagation/dissipation. The rest of the paper considers a cluster of the high-T phase in the UV in coexistence with the low-T phase, in a simplified ansatz in which the wall separating them is positioned only in the holographic coordinate. This allows to find the force o…
We establish a holographic bottom-up model which covers both the baryonic and quark matter phases in cold and dense QCD. This is obtained by including the baryons using simple approximation schemes in the V-QCD model, which also includes the backreaction of the quark matter to the dynamics of pure Yang-Mills. We examine two approaches for homogeneous baryon matter: baryons as a thin layer of noninteracting matter in the holographic bulk, and baryons with a homogeneous bulk gauge field. We find that the second approach exhibits phenomenologically reasonable features. At zero temperature, the va…
We study nucleon-to-delta electromagnetic transition form factors and relations between them within the framework of holographic dual model of QCD proposed by Sakai and Sugimoto. In this setup, baryons appear as topological solitons of the five dimensional holographic gauge theory that describes a tower of mesons and their interactions. We find a relativistic extension of the nucleon-delta-vector meson interaction vertices and use these to calculate transition form factors from holographic QCD. We observe that at low momentum transfer, magnetic dipole, electric and Coulomb quadrupole form fact…
Recent progress in constructing holographic models for QCD is discussed, concentrating on the bottom-up models which implement holographically the renormalization group flow of QCD. The dynamics of gluons can be modeled by using a string-inspired model termed improved holographic QCD, and flavor can be added by introducing space filling branes in this model. The flavor fully backreacts to the glue in the Veneziano limit, giving rise to a class of models which are called V-QCD. The phase diagrams and spectra of V-QCD are in good agreement with results for QCD obtained by other methods.
We study holographically the zero and finite temperature behavior of the potential energy and holographic subregion complexity corresponding to a probe meson in a non-conformal model. We observe that in zero and low temperature non-conformality has a decreasing effect on the dimensionless meson potential energy. However, non-conformal corrections increase absolute value of the dimensionless holographic subregion complexity in both zero and finite temperature which means the non-conformal state needs less information to be specified. In other words, considering the effect of non-conformality, t…
Properties of the tensor glueball are discussed in the Witten-Sakai-Sugimoto Model, a top-down holographic approach to the non-perturbative region of Quantum Chromodynamics (QCD).
We review the holographic approach to electromagnetic phenomena in large N QCD. After a brief discussion of existing holographic models, we concentrate on the improved holographic QCD model extended to include magnetically induced phenomena. We explore the influence of magnetic fields on the QCD ground state, focusing on (inverse) magnetic catalysis of chiral condensate, investigate the phase diagram of the theory as a function of magnetic field, temperature and quark chemical potential, and, finally discuss effects of magnetic fields on the quark-anti-quark potential, shear viscosity, speed o…
We study topological objects in holographic QCD based on the Sakai-Sugimoto model, which is constructed with $N_c$ D4 branes and $N_f$ D8/$\bar{\rm D8}$ branes in the superstring theory, and is infrared equivalent to 1+3 dimensional massless QCD. Using the gauge/gravity duality, holographic QCD is described as 1+4 dimensional U($N_f$) gauge theory in flavor space with a background gravity, and its instanton solutions correspond to baryons. First, using the Witten Ansatz, we reduce holographic QCD into a 1+2 dimensional Abelian Higgs theory in a curved space and consider its topological aspect.…
We have constructed a noncommutative deformation of the holographic QCD (Sakai-Sugimoto) model and evaluated the mass spectrum of low spin vector mesons at finite temperature. The masses of light vector- and pseudovector-meson in the noncommutative holographic QCD model reduces over the whole area in the intermediate-temperature regime compared to the commutative case. However, the space noncommutativity does not change the properties of temperature dependence for the mass spectrum of low spin mesons. The masses of meson also decrease with increasing temperature in noncommutative case.
In this paper we study the dynamical instability of Sakai-Sugimoto's holographic QCD model at finite baryon density. In this model, the baryon density, represented by the smeared instanton on the worldvolume of the probe D8-\overline{D8} mesonic brane, sources the worldvolume electric field, and through the Chern-Simons term it will induces the instability to form a chiral helical wave. This is similar to Deryagin-Grigoriev-Rubakov instability to form the chiral density wave for large N_c QCD at finite density. Our results show that this kind of instability occurs for sufficiently high baryon …
Recently certain nonlocal operators were proposed to provide quark masses for the holographic model of QCD developed by Sakai and Sugimoto. The properties of these operators at strong coupling are examined in detail using holographic techniques. We find the renormalization procedure for these operators is modified by the running of the five-dimensional gauge coupling. We explicitly evaluate the chiral condensate characterized by these operators.
The H-dibaryon (uuddss) is studied in holographic QCD for the first time. In holographic QCD, four-dimensional QCD, i.e., SU($N_c$) gauge theory with chiral quarks, can be formulated with $S^1$-compactified D4/D8/$\overline{\rm D8}$-brane system. In holographic QCD with large $N_c$, all the baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons, and the H-dibaryon can be described as an SO(3)-type topological soliton with $B=2$. We derive the low-energy effective theory to describe the H-dibaryon in holographic QCD. The H-dibaryon mass is found to be …
We consider a holographic model of QCD, obtained by a very simple modification of the original construction, which describes at the same time the pion mass, the QCD anomalies and the baryons as topological solitons. We study in detail its phenomenological implications in both the mesonic and baryonic sectors and compare with the observations.
We study solitons in the context of Sakai-Sugimoto-Witten holographic model of QCD. In the large 't Hooft coupling limit, flat space instantons give an approximate description of baryons. We provide an ansatz through deforming the BPST instanton by zero modes and obtain a subleading correction to the effective action. We also consider the quantum mechanical description of the collective coordinates. The correction term appears as a perturbation to the potential of the Hamiltonian and hence we can derive a first order correction to the mass spectrum of baryons.
We investigate the response of dense and hot holographic QCD (hQCD) to a static and baryonic electric field E using the chiral model of Sakai and Sugimoto. Strong fields with E>(\sqrtλM_{KK})^2 free quark pairs, causing the confined vacuum and matter state to decay. We generalize Schwinger's QED persistence function to dense hQCD. At high temperature and density, Ohm's law is derived generalizing a recent result by Karch and O'Bannon to the chiral case.
We examine instantons and solitons of the effective action of probe D8-branes in the background of $N_c$ D4-branes which has served as a holographic description of QCD. We show that the 4d instantons sit at the minimum of the Euclidean 5d action. Restricting to the static solitons of the five-dimensional model we are led to consider monopoles in a 3-dimensional curved space. Since the background metric depends only on the fifth coordinate, it is possible to reduce the monopole equations to the ones in flat space and write down the explicit solutions.
We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. The kinetic gauge function can be fixed by requesting the linear Regge spectrum of mesons. We calculate the free energy to obtain the phase diagram of the holographic QCD model and interpret our result as the heavy quarks system by comparing the recent lattice QCD simulation. We finally obtain the equations of state in our model.
We review construction of the improved holographic models for QCD-like confining gauge theories and their applications to the physics of the Quark-gluon plasma. We also review recent progress in this area of research. The lecture notes start from the vacuum structure of these theories, then develop thermodynamic and hydrodynamic observables and end with more advanced topics such as the holographic QCD in the presence of external magnetic fields. This is a summary of the lectures presented at the 56th Cracow School of Theoretical Physics in Spring 2016 at Zakopane, Poland.
Quantization Rules in Holographic QCD Models
本文利用 WKB 近似推导全息 QCD 模型准稳态的广义 Bohr-Sommerfeld 量子化规则，并应用于 soft wall 模型计算标量场与矢量场的准正常模，为理解解离过程提供见解。
We consider configurations of D4-D8-\bar D8 branes which correspond to large N QCD with non-vanishing temperature and chemical potential for baryon number and isospin. We study the holographic dual of this model and find a rich phase structure. The phases, distinguished by the values of quark condensates, are separated by the surfaces of first order phase transitions. The picture is in many respects similar to the expected phase structure of QCD in the chiral limit.
Gravitational form factors of pion from top-down holographic QCD
首次利用自顶向下全息QCD方法计算了介子引力形状因子，获取了D项，并发现介子通过无限胶球谱进行引力相互作用的胶球主导现象。
Based on the expectation that constituent quark model may capture right physics in the large N limit, we point out that orbital angular momentum of the quark-antiquark pair inside light mesons of low spins in the constituent quark model may provide a clue for the holographic dual string model of large N QCD. Our discussion, relying on a few suggestive assumptions, leads to a necessity of world-sheet fermions in the bulk of dual strings that can incorporate intrinsic spins of fundamental QCD degrees of freedom. We also comment on an interesting issue of the size of mesons in the context of holo…
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