We review baryons in the D4-D8 holographic model of low energy QCD, with the large $N_c$ and the large 't Hooft coupling limit. The baryon is identified with a bulk soliton of a unit Pontryagin number, which from the four-dimensional viewpoint translates to a heavily modified Skyrmion dressed by condensates of spin one mesons. We explore classical properties and find that the baryon in the holographic limit is amenable to an effective field theory description. We also present a simple method to capture all leading and subleading interactions in the $1/N_c$ and the derivative expansions. An infinitely predictive model of baryon-meson interactions is thus derived, although one may trust results only for low energy processes, given various approximations in the bulk. We showcase a few comparisons to experiments, such the leading axial couplings to pions, the leading vector-like coupling, and a qualitative prediction of the electromagnetic vector dominance that involves the entire tower of vector mesons. (This article is an expanded version of a proceeding contribution to "30 years of mathematical method in high energy physics," Kyoto 2008)
We numerically simulate collisions of charged shockwaves in Einstein-Maxwell theory in anti-de Sitter space as a toy model of heavy ion collisions with non-zero baryon charge. The stress tensor and the baryon current become well described by charged hydrodynamics at roughly the same time. The effect of the charge density on generic observables is typically no larger than 15\%. %The rapidity profile of the charge is wider than the profile of the local energy density. We find significant stopping of the baryon charge and compare our results with those in heavy ion collision experiments.
We study how monopole catalysis of baryon decay is realized in holographic QCD. Physics of monopole catalysis becomes much simpler in holographic description as it occurs due to the violation of the Bianchi identity for the 5D gauge symmetry when magnetic monopole is present. In holographic QCD we find a unified picture of the baryon number violation under magnetic monopole or electroweak sphaleron, giving a new mechanism of baryon number violation. We also embed our set-up in the string theory model by Sakai and Sugimoto.
We construct the D4/D8 brane configuration in the Witten-Sakai-Sugimoto model by introducing a pair of heavy flavour brane with a heavy-light open string. The multiplets created by the heavy-light string acquire mass due to the finite separation of the heavy and light flavour branes thus they could be identified as the heavy-light meson fields in this model. On the other hand the glueball field is identified as the gravitational fluctuations carried by the close string in the bulk, so this model is able to describe the interaction of glueball and heavy-light meson through the open-close string…
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 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 consider a holographic model constructed from an intersecting brane configuration $D4/D4/\bar{D4}$ in noncritical string theory. We study the baryon in the confined phase of this supergravity by considering the source term for the baryon. Also, the thermodynamics functions are studied. Moreover, we obtain the binding energy of the baryon in this holographic QCD-like model.
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.
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…
Studying the Witten-Sakai-Sugimoto model with type IIA string theory, we find the glueball-baryon interaction is predicted in this model. The glueball is identified as the 11D gravitational waves or graviton described by the M5-brane supergravity solution. Employing the relation of M-theory and type IIA string theory, glueball is also 10D gravitational perturbations which are the excited modes by close strings in the bulk of this model. On the other hand, baryon is identified as a D4-brane wrapped on $S^{4}$ which is named as baryon vertex, so the glueball-baryon interaction is nothing but the…
We propose a mean-field approach to analyze many-body systems of fermions in the gauge/gravity duality. We introduce a non-vanishing classical fermionic field in the gravity dual, which we call the holographic mean field for fermions. The holographic mean field takes account of the many-body dynamics of the fermions in the bulk. The regularity condition of the holographic mean field fixes the relationship between the chemical potential and the density unambiguously. Our approach provides a new framework of gauge/gravity duality for finite-density systems of baryons in the confinement phase.
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.
In the holographic model of QCD suggested by Sakai and Sugimoto, baryons are chiral solitons sourced by D4 instantons in bulk of size 1/\sqrtλ with λ=g^2N_c. We quantize the D4 instanton semiclassically using \hbar=1/(N_cλ) and non-rigid constraints on the vector mesons. The holographic baryon is a small chiral bag in the holographic direction with a Cheshire cat smile. The vector-baryon interactions occur at the core boundary of the instanton in D4. They are strong and of order 1/\sqrt{\hbar}. To order \hbar^0 the electromagnetic current is entirely encoded on the core boundary and vector-mes…
This is a contribution for the Proceedings of the Conference Hot Quarks 2016, held at South Padre Island, Texas, USA, 12-17 September 2016. I briefly review some thermodynamic and baryon transport results obtained from a bottom-up Einstein-Maxwell-Dilaton holographic model engineered to describe the physics of the quark-gluon plasma at finite temperature and baryon density. The results for the equation of state, baryon susceptibilities, and the curvature of the crossover band are in quantitative agreement with the corresponding lattice QCD results with $2+1$ flavors and physical quark masses. …
In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang-Mills instantons, whose solutions can be obtained from the celebrated ADHM construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a r…
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.
We describe a new exact relation for large $N_c$ QCD for the long-distance behavior of baryon form factors in the chiral limit. This model-independent relation is used to test the consistency of the structure of several baryon models. All 4D semiclassical chiral soliton models satisfy the relation, as does the Pomarol-Wulzer holographic model of baryons as 5D Skyrmions. However, remarkably, we find that the holographic model treating baryons as instantons in the Sakai-Sugimoto model does not satisfy the relation.
We study the energy dispersions of holographic light mesons and their decay constants on dense nuclear medium. As the spatial momenta of mesons along the boundary direction increase, both observables of the mesons not only increase but also split according to the isospin charges. The decay constant of the negative meson is more large than that of the positive meson of the same type due to the chemical potentials of the background nucleons.
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…
We consider the photo-excitation of charm and bottom pentaquarks with the holographic assignments $[\frac 12\frac 12^-]_{S=0,1}$ and $[\frac 12\frac 32^-]_{S=1}$, in the photo-production of heavy vector mesons such as charmonia and bottomonia near threshold. We use a Witten diagram to combine the s-channel photo-excitation of holographic pentaquarks with a massive t-channel graviton or tensor glueball exchange, to extract the scattering amplitude for heavy meson photo-production in the threshold region. The pentaquark signal is too weak to be detected at current electron facilities.
We study fluctuations of a U(1) gauge field on the worldvolume of Nf probe D7-branes in the background of Nc black D3-branes with a finite baryon density. The choice of mode corresponds to vector mesons in the dual gauge theory whose mass and lifetime can be determined by a study of the quasinormal modes. The speed of propagation of these holographic mesons at large momenta is studied from the dispersion relations of the quasinormal modes of the system.
We propose a new matrix model describing multi-baryon systems. We derive the action from open string theory on the wrapped baryon vertex D-branes embedded in the D4-D8 model of large N holographic QCD. The positions of k baryons are unified into k x k matrices, with spin/isospin of the baryons encoded in a set of k-vectors. Holographic baryons are known to be very small in the large 't Hooft coupling limit, and our model offers a better systematic approach to dynamics of such baryons at short distances. We compute energetics and spectra (k=1), and also short-distance nuclear force (k=2). In pa…
We study the conductivity, susceptibility and diffusion of a strongly coupled quark gluon plasma from the holographic perspective. We calculate general expressions for these quantities in the presence of finite baryon density and show that in this context, for the D3/D7 intersection the Einstein relation holds, providing another non-trivial check of the holographic correspondence at finite temperature.
We discuss homogeneous baryonic matter in the decompactified limit of the Sakai-Sugimoto model, improving existing approximations based on flat-space instantons. We allow for an anisotropic deformation of the instantons in the holographic and spatial directions and for a density-dependent distribution of arbitrarily many instanton layers in the bulk. Within our approximation, the baryon onset turns out to be a second-order phase transition, at odds with nature, and there is no transition to quark matter at high densities, at odds with expectations from QCD. This changes when we impose certain …
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 properties of the Sakai-Sugimoto model at finite magnetic field and baryon chemical potentials. We show that in a finite magnetic field, there exists a spatially homogeneous configuration carrying finite baryon number density. At low magnetic field and baryon chemical potential the equation of state of the matter coincides with that obtained from the chiral perturbation theory Lagrangian with an anomalous term. We discuss the behavior of the system at larger magnetic fields.
Within a holographic framework, we consider vector mesons riding on a gravity-dilaton background. The latter one is determined directly from a Schrödinger equivalent potential which delivers a proper $ρ$ meson Regge trajectory. The mapping on the dilaton potential yields a thermodynamic phase structure with a first-order transition.
We study the di-baryon in the holographic QCD. The di-baryon is composed of six quarks and bound by the color interaction. In this paper, we adopt the Sakai-Sugimoto (SS) model as the holographic QCD to study the di-baryon. The SS model is formulated in a $\mathrm{D4}/\mathrm{D8}/\overline{\mathrm{D8}}$ system of the Type IIA string theory. It is expected that the di-baryon is described by the 2-instanton configuration of the flavor symmetry on D8-branes since the baryon number is identified as the instanton number. We will construct the 't Hooft 2-instanton solution explicitly and use it to d…
We study the decay process of large-spin mesons in the context of the gauge/string duality, using generic properties of confining backgrounds and systems with flavour branes. In the string picture, meson decay corresponds to the quantum-mechanical process in which a string rotating on the IR "wall" fluctuates, touches a flavour brane and splits into two smaller strings. This process automatically encodes flavour conservation as well as the Zweig rule. We show that the decay width computed in the string picture is in remarkable agreement with the decay width obtained using the phenomenological …
In this paper we study D-brane scalar fluctuations in global Pilch-Warner background geometry. We consider configurations of the probe branes compatible with the kappa symmetry preserving condition and the brane classical equations of motion. The corresponding meson spectra, obtained by the fluctuations along the transverse brane directions, admit equidistant structure for the higher modes, but some of them show additional shifts in their ground states.
We revisit holographic mesons in the D4/D6 model to study holographic light vector mesons and the properties of heavy quarkonium in confining and deconfining phases. To treat the light mesons and heavy quarkonium on the same footing, we use the same compactification scale MKK in both systems. We observe that like scalar and pseudo-scalar mesons the vector meson mass is linearly proportional to the square root of the quark mass, when the quark mass is large. With a MKK fixed by light meson masses, we calculate the mass of heavy quarkonium in confining and deconfining phases. We also obtain the …
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 propose a holographic model of baryon interactions based on non-supersymmetric D7-anti-D7 flavor branes embedded in the Klebanov-Strassler background. The baryons are D3-branes wrapping the 3-sphere of the conifold with M strings connecting the D3 and the flavor branes. Depending on the location of the latter there are two possibilities: the D3 either remains separate from the flavor branes or dissolves in them and becomes a flavor instanton. The leading order interaction between the baryons is a competition between the attraction and the repulsion due to the sigma and omega mesons. The lig…
We investigate masses and coupling constants of mesons and nucleons within a hard wall model of holographic QCD in a unified approach. We first examine an appropriate form of fermionic solutions by restricting the mass coupling for the five dimensional bulk fermions and bosons. We then derive approximated analytic solutions for the nucleons and the corresponding masses in a small mass coupling region. In order to treat meson and nucleon properties on the same footing, we introduce the same infrared (IR) cut in such a way that the meson-nucleon coupling constants, i.e., g_{pi NN} and g_{rho NN}…
We study two $1/N_c$ effects on the meson spectra by using the AdS/CFT correspondence where the $1/N_c$ corrections from the chiral condensate and the quark density are controlled by the gravitational backreaction of the massive scalar field and U(1) gauge field respectively. The dual geometries with zero and nonzero current quark masses are obtained numerically. We discuss meson spectra and binding energy of heavy quarkonium with the subleading corrections in the hard wall model.
A holographic model of probe vector mesons (quarkonia) is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The vector meson action is modified to account for various quark masses. We focus on the $Φ$, $J/ψ$ and $Υ$ meson melting in agreement with hadron phenomenology in heavy-ion collisions at LHC, that is the formation of hadrons at the observed freeze-out temperature of 155 MeV.
We consider the chiral condensate in the baryonic dense medium using the generalized Sakai-Sugimoto model. It is defined as the vacuum expectation value of open Wilson line that is proposed to be calculated by use of the area of world-sheet instanton. We evaluate it in confined as well as deconfined phase. In both phases, the chiral condensate has a minimum as a function of baryon density. In the deconfined phase, taking into account the chiral symmetry restoration, we classify the behavior of chiral condensate into three types. One can set the parameter of the theory such that the results, in…
Within the framework of a holographic dual model of QCD, we develop a formalism for calculating form factors of vector mesons. We show that the holographic bound states can be described not only in terms of eigenfunctions of the equation of motion, but also in terms of conjugate wave functions that are close analogues of quantum-mechanical bound state wave functions. We derive a generalized VMD representation for form factors, and find a very specific VMD pattern, in which form factors are essentially given by contributions due to the first two bound states in the Q^2-channel. We calculate ele…
A new method to study nuclear physics via holographic QCD is proposed. Multiple baryons in the Sakai-Sugimoto background are described by a matrix model which is a low energy effective theory of D-branes of the baryon vertices. We study the quantum mechanics of the matrix model and calculate the eigenstates of the Hamiltonian. The obtained states are found to coincide with known nuclear and baryonic states, and have appropriate statistics and charges. Calculated spectra of the baryon/nucleus for small baryon numbers show good agreement with experimental data. For hyperons, the Gell-Mann--Okubo…
In this paper, we study properties of baryons by using a holographic dual of QCD on the basis of the D4/D8-brane configuration, where baryons are described by a soliton. We first determine the asymptotic behavior of the soliton solution, which allows us to evaluate well-defined currents associated with the U(N_f)_L \times U(N_f)_R chiral symmetry. Using the currents, we compute static quantities of baryons such as charge radii and magnetic moments, and make a quantitative test with experiments. It is emphasized that not only the nucleon but also excited baryons, such as Δ, N(1440), N(1535) etc…
We study baryons of arbitrary isospin in a stringy holographic QCD model. In this D4-D8 holographic setting, the flavor symmetry is promoted to a gauge symmetry in the bulk, and produces, as KK modes of the gauge field, pions and spin one mesons of low energy QCD. Baryons of arbitrary isospins are represented as instanton solitons with isospin and spin quantum numbers locked, in a manner similar to the Skyrmion model. The soliton picture leads to a natural effective field theory of arbitrary baryons interacting with mesons. Couplings of baryons to axial mesons, including pions, are dominated i…
We show that holographic models of QCD predict the presence of a Chern-Simons coupling between vector and axial-vector mesons at finite baryon density. In the AdS/CFT dictionary, the coefficient of this coupling is proportional to the baryon number density, and is fixed uniquely in the five-dimensional holographic dual by anomalies in the flavor currents. For the lightest mesons, the coupling mixes transverse $ρ$ and $a_1$ polarization states. At sufficiently large baryon number densities, it produces an instability, which causes the $ρ$ and $a_1$ mesons to condense in a state breaking both ro…
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…
We study the spectrum of scalar mesons in the holographic dual of walking technicolor, obtained by embedding D7 - anti-D7 probe branes in a certain type IIB background. The scalar mesons arise from fluctuations of the probe techniflavour branes and complement the (axial-)vector meson spectra that we investigated in earlier work. By explicitly finding the spectrum of scalar masses, we show that the nonsupersymmetric D7 - anti-D7 embedding is stable with respect to such fluctuations. Interestingly, it turns out that the mass splitting between the scalar and vector meson spectra is of subleading …
The response function of a homogeneous and dense hadronic system to a time-dependent (baryon) vector potential is discussed for holographic dense QCD (D4/D8 embedding) both in the confined and deconfined phases. Confined holographic QCD is an uncompressible and static baryonic insulator at large N_c and large λ, with a gapped vector spectrum and a massless pion. Deconfined holographic QCD is a diffusive conductor with restored chiral symmetry and a gapped transverse baryonic current. Similarly, dense D3/D7 is diffusive for any non-zero temperature at large N_c and large λ. At zero temperature …
We develope the holographic mean field theory approach in a bottom-up holographic QCD model including baryons and scalar mesons in addition to vector mesons and pions. We study the effect of parity doubling structure of baryons at non-zero density to the equation of state between the chemical potential and the baryon number density. We first show that we can adjust the amount of nucleon mass coming from the chiral symmetry breaking by changing the boundary value of the five-dimensional baryon fields. Then, introducing the mean field for the baryon fields, we calculate the equation of state bet…
We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature of such computations is explained, thanks to the well-understood nature of confining string backgrounds, and two different examples of the calculation in given backgrounds are used to illustrate the details. The effect we discover, whilst only qualitative, is re-obtainable in many such examples, in four-point but also higher point amplitudes.
We perform the first study of baryons in holographic QCD with $D4/D8/\bar{D8}$ multi-$D$ brane system in type IIA superstring theory. The baryon is described as a chiral soliton solution in the four-dimensional meson effective action derived from holographic QCD. We also present a brief review of the holographic model from the viewpoints of recent hadron physics and QCD phenomenologies.
Employing the asymptotic instanton solution in an arbitrary background of a set of holographic QCD models, we show that baryon form factors have a precise large-distance behaviour regardless of the background. The dependence coincides with that obtained from general chiral soliton models and large-$N_C$ chiral perturbation theory. The nonlinear terms in the equations of motion are necessary to recover the correct results. We also show that the holographic currents have the right structure at low energy if the solutions of the full equation of motion, instead of the linearized ones, are used. T…
We introduce the strange quark mass to the Sakai-Sugimoto model of holographic QCD. We compute mass shifts in the spectra of three-flavor baryons at the leading order in perturbation in quark masses. Comparison with experimental data shows an agreement only qualitatively.
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…
In the context of gauge/gravity duals with flavor, we examine heavy-light mesons which involve a heavy and a light quark. For this purpose we embed two D7 brane probes at different positions into the gravity background. We establish the non-Abelian Dirac-Born-Infeld (DBI) action for these probes, in which the U(2) matrix describing the embedding is diagonal. The fluctuations of the brane probes correspond to the mesons. In particular, the off-diagonal elements of the U(2) fluctuation matrix correspond to the heavy-light mesons, while the diagonal elements correspond to the light-light and heav…
We consider aspects of dynamical baryons in a holographic dual of QCD that is proposed on the basis of a D4/D8-brane configuration. We construct a soliton solution carrying a unit baryon number and show that it is given by an instanton solution of four-dimensional Yang-Mills theory with fixed size. The Chern-Simons term on the flavor D8-branes plays a crucial role of protecting the instanton from collapsing to zero size. By quantizing the collective coordinates of the soliton, we work out the baryon spectra. Negative-parity baryons as well as baryons with higher spins and isospins can be obtai…
We calculate elastic and non-elastic electromagnetic form factors for vector and axial-vector mesons in the holographic D4-D8 brane model. We obtain the mass spectrum and Regge trajectories for these particles. From the elastic form factors we extract the electric radius, the magnetic and quadrupole moments. Form factors for transverse and longitudinal polarizations are also obtained. We find superconvergence sum rules for the vector and axial-vector meson couplings that determine the asymptotic behavior of the form factors at large momentum transfer. Our results show good agreement with other…
We study the relationship between chiral symmetry breaking and baryons in holographic QCD. We construct a soliton with unit baryon charge in the presence of a nonzero mean value of the scalar bifundamental field, which is dual to the chiral condensate. We obtain a relation between the chiral condensate and the mass of the baryon and find in a clear-cut way that at large values of the condensate the holographic soliton is no longer located on the IR wall. Instead it is split into two halves, which are symmetrically located on the left and right flavor branes. On the other hand we find that the …
