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 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 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 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.
It has been believed for a long time that the tensionless limit of superstring theory can be described by a higher spin gauge theory. Recently, a concrete realization of this idea was proposed via 3d Aharony-Bergman-Jafferis (ABJ) theory with the help of holographic duality. In this note we review our work on finding a similar relation involving 2d coset type models. We start by proposing and examining holographic dualities between 3d higher spin gauge theories with matrix valued fields and the large N limit of 2d coset type models. After that we discuss possible relations to superstring theor…
In this paper we will show some applications achieved within type IIB superstring backgrounds since the emergence of the AdS/CFT correspondence. This correspondence relates a super Yang-Mills (SYM) theory, with strong coupling, and a type IIB superstring theory, with weak coupling. The use of the AdS/CFT correspondence allows us to investigate many aspects of hadronic physics described by QCD outside the perturbative regime, for example, glueball masses and the Regge trajectories related to the pomeron and the odderon. Throughout the text we will deal with the AdS/CFT correspondence within the…
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 …
Based on the holographic conjecture for superstrings on Dp-brane backgrounds and the dual (p+1)-dimensional gauge theory ($0\le p\le 4$) given in hep-th/0308024 and hep-th/0405203, we continue the study of superstring amplitudes including string higher modes ($n\ne 0$). We give a prediction to the two-point functions of operators with large R-charge J. The effect of stringy modes do not appear as the form of anomalous dimensions except for p=3. Instead, it gives non-trivial correction to the two-point functions for supergravity modes. For p=4, the scalar two-point functions for any n behave li…
The Sakai-Sugimoto model is the most pre-eminent model of holographic QCD, in which baryons correspond to topological solitons in a five-dimensional bulk spacetime. Recently it has been shown that a single soliton in this model can be well approximated by a flat-space self-dual Yang-Mills instanton with a small size, although studies of multi-solitons and solitons at finite density are currently beyond numerical computations. A lower-dimensional analogue of the model has also been studied in which the Sakai-Sugimoto soliton is replaced by a baby Skyrmion in three spacetime dimensions with a wa…
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 study holographic models of the QCD temperature-chemical potential phase diagram based on the D3/D7 system with chiral symmetry breaking. The baryonic phase may be included through linked D5-D7 systems. In a previous analysis of a model with a running gauge coupling a baryonic phase was shown to exist to arbitrarily large chemical potential. Here we explore this phase in a more generic phenomenological setting with a step function dilaton profile. The change in dilaton generates a linear confining $\bar{q}q$ potential and opposes the screening effect of temperature. We show that the persist…
We study baryonic matter in holographic QCD with D4/D8/\bar{D8} multi-D brane system in type IIA superstring theory. The baryon is described as the "brane-induced Skyrmion", which is a topologically non-trivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the "truncated-resonance model" approach for the baryon analysis, including pion and ρmeson fields below the ultraviolet cutoff scale M_KK \sim 1GeV, to keep the holographic duality with QCD. We describe the baryonic matter in large N_c as single brane-induced Skyrmion on the three-dimens…
We study baryonic matter with isospin asymmetry, including fully dynamically its interplay with pion condensation. To this end, we employ the holographic Witten-Sakai-Sugimoto model and the so-called homogeneous ansatz for the gauge fields in the bulk to describe baryonic matter. Within the confined geometry and restricting ourselves to the chiral limit, we map out the phase structure in the presence of baryon and isospin chemical potentials, showing that for sufficiently large chemical potentials condensed pions and isospin-asymmetric baryonic matter coexist. We also present first results of …
We discuss the effect of baryonic matter on the zero-temperature chiral phase transition at finite chemical potential in the presence of a background magnetic field. The main part of our study is done in the deconfined geometry of the Sakai-Sugimoto model, i.e., at large N_c and strong coupling, with non-antipodal separation of the flavor branes. We find that for not too large magnetic fields baryonic matter completely removes the chiral phase transition: chirally broken matter persists up to arbitrarily large chemical potential. At sufficiently large magnetic fields, baryonic matter becomes d…
In this note we discuss a possible holographic dual of the two dimensional conformal field theory associated with the world-sheet of a macroscopic superstring in a compactification on four-torus. We assume the near horizon geometry of the black string has symmetries of $AdS_3\times S^3\times T^4$ and construct a sigma model in the bulk. Analyzing the symmetries of the bulk theory and comparing them with those of the CFT in a special light-cone gauge we find agreement between global symmetries. Due to non-standard gauge realization it is not clear how affine symmetries can be realized.
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 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.
Using exact boundary conformal field theory methods we analyze the D-brane physics of a specific four-dimensional non-critical superstring theory which involves the N=2 SL(2)/U(1) Kazama-Suzuki model at level 1. Via the holographic duality of hep-th/9907178 our results are relevant for D-brane dynamics in the background of NS5-branes and D-brane dynamics near a conifold singularity. We pay special attention to a configuration of D3- and D5-branes that realizes N=1 supersymmetric QCD and discuss the massless spectrum and classical moduli of this setup in detail. We also comment briefly on the i…
We study the ground state of baryonic/axial matter at zero temperature chiral-symmetry broken phase under a large magnetic field, in the framework of holographic QCD by Sakai-Sugimoto. Our study is motivated by a recent proposal of chiral magnetic spiral phase that has been argued to be favored against previously studied phase of homogeneous distribution of axial/baryonic currents in terms of meson super-currents dictated by triangle anomalies in QCD. Our results provide an existence proof of chiral magnetic spiral in strong coupling regime via holography, at least for large axial chemical pot…
We investigate the holographic correspondence between (p+1)-dimensional ($0\le p\le 4$) SYM theories with 16 supercharges and superstring theories on the near-horizon limit of Dp-brane backgrounds. Following an approach based on the tunneling picture, we study Euclidean superstring semi-classically along null geodesics which connect two points on the boundary of the spacetime. We extend the analysis of hep-th/0308024 and study the fermionic sector of the superstring. For $p\ne 3$, we do not have world-sheet supersymmetry, and the energies of bosonic and fermionic fluctuations do not match. By …
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
We review recent progress in the study of non-rational (boundary) conformal field theories and their applications to describe exact holographic backgrounds in superstring theory. We focus mainly on the example of the supersymmetric coset SL(2,R)/U(1), corresponding to the two-dimensional black hole, and its dual N=2 Liouville. In particular we discuss the modular properties of their characters, their partition function as well as the exact boundary states for their various D-branes. Then these results are used to construct the corresponding quantities in the CFT of the NS5-brane background, wi…
We holographically investigate the decay of heavy-flavoured baryonic hadron involving glueball by using the Witten-Sakai-Sugimoto model. Since baryon in this model is recognized as the D4-brane wrapped on $S^{4}$ and the glueball field is identified as the bulk gravitational fluctuations, the interaction of the bulk graviton and the baryon brane could be naturally interpreted as glueball-baryon interaction through the holography which is nothing but the close-open string interaction in string theory. In order to take account into the heavy flavour, an extra pair of heavy-flavoured branes separ…
Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai-Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang-Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues…
We study the thermodynamical phase structures of holographic QCD with nontrivial topologically charged domain-wall/membranes which are originally related to the multiple $θ$-vacua in the large $N_c$ limit. We realize the topologically charged membranes as the holographic D6-brane fluxes in the Sakai-Sugimoto model. The D6-brane fluxes couple to the probe D8-anti-D8 via Chern-Simon term, and act as the source for the baryonic current density of QCD. We find rich phase structures of the dual meson system by varying asymptotic separation of D8 and anti-D8. Especially, there can be a thermodynamic…
We investigate the Sakai-Sugimoto model at nonzero baryon chemical potential in a background magnetic field both in the confined phase and in the deconfined phase with restored chiral symmetry. In this case the 8-brane Chern-Simons term becomes important. In the confined phase it generates a gradient of the pseudo-scalar "pion", which carries a non-vanishing baryon charge. Above a critical value of the chemical potential there is a second order phase transition to a mixed phase which includes also ordinary baryonic matter. However, at fixed baryon charge density the matter is purely "pion"-gra…
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 describe the simplest example of an instanton bag in Euclidean space. It consists of a monopole wall and a Kaluza-Klein monopole wall, lifted to one higher dimension, trapping the instanton charge in the middle. This object has finite instanton density in a three-dimensional volume. Baryon physics in holographic QCD models gets translated into a multi-instanton problem in the bulk, and a state with a high density baryonic charge consists of a non-diluted multi-instanton solution. The instanton bag is a good candidate for this high-density state. We compute its parameters via moduli stabiliz…
We study a non-standard decoupling limit of the D1/D5-brane system, which interpolates between the near-horizon geometry of the D1/D5 background and the near-horizon limit of the pure D5-brane geometry. The S-dual description of this background is actually an exactly solvable two-dimensional (worldsheet) conformal field theory: {null-deformed SL(2,R)} x SU(2) x T^4 or K3. This model is free of strong-coupling singularities. By a careful treatment of the SL(2,R), based on the better-understood SL(2,R) / U(1) coset, we obtain the full partition function for superstrings on SL(2,R) x SU(2) x K3. …
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 discuss a scenario that the dark matter in late time universe emerges as part of the holographic stress-energy tensor on the hypersurface in higher dimensional flat spacetime. Firstly we construct a toy model with a de Sitter hypersurface as the holographic screen in the flat bulk. After adding the baryonic matter on the screen, we assume that both of the dark matter and dark energy can be described by the Brown-York stress-energy tensor. From the Hamiltonian constraint equation in the flat bulk, we find an interesting relation between the dark matter and baryonic matter's energy density pa…
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 the Regge trajectories of holographic mesons and baryons by considering rotating strings and D5 brane, which is introduced as the baryon vertex. Our model is based on the type IIB superstring theory with the background of asymptotic $AdS_5\times S^5$. This background is dual to a confining supersymmetric Yang-Mills theory (SYM) with gauge condensate, $<F^2>$, which determines the tension of the linear potential between the quark and anti-quark. Then the slope of the meson trajectory ($α'_{M}$) is given by this condensate as $α'_{M}=1/\sqrt{π<F^2>}$ at large spin $J$. This relation is …
Recently, a homogeneous ansatz has been used to study cold dense nuclear matter in the Sakai-Sugimoto model of holographic QCD. To justify this homogeneous approximation we here investigate a homogeneous ansatz within a low-dimensional toy version of Sakai-Sugimoto to study finite baryon density configurations and compare it to full numerical solutions. We find the ansatz corresponds to enforcing a dyon salt arrangement in which the soliton solutions are split into half-soliton layers. Within this ansatz we find analogues of the proposed baryonic popcorn transitions, in which solutions split i…
We study the dense nuclear matter within the holographic Sakai-Sugimoto model. The nuclear matter is described via instantons in bulk, whose size has the new temperature dependency. Then, properties of nuclear matter have been studied for different temperatures. For example, free energy and baryon density are examined for different temperature values. Also, nuclear matter properties, like the speed of sound and connection of nuclear matter and quark matter, are discussed. As we have increased the temperature, the phase transition value has been changed from baryon to quark, which is non-physic…
We study the response of the Sakai-Sugimoto holographic model of large N_c QCD at nonzero temperature to external electric and magnetic fields. In the electric case we find a first-order insulator-conductor transition in both the confining and deconfining phases of the model. In the deconfining phase the conductor is described by the parallel 8-brane-anti-8-brane embedding with a current of quarks and anti-quarks. We compute the conductivity and show that it agrees precisely with a computation using the Kubo formula. In the confining phase we propose a new kind of 8-brane embedding, correspond…
We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant bary…
In the large N limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of "popcorn" transitions upon increasing the density. Through these transitions normal (3D) lattices …
Large-N_c QCD matter at intermediate baryon density and low temperatures has been conjectured to be in the so-called quarkyonic phase, i.e., to have a quark Fermi surface and on top of it a confined spectrum of excitations. It has been suggested that the presence of the quark Fermi surface leads to a homogeneous phase with restored chiral symmetry, which is unstable towards creating condensates breaking both the chiral and translational symmetry. Motivated by these exotic features, we investigate properties of cold baryonic matter in the single flavor Sakai-Sugimoto model searching for a holog…
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 extend our investigation of resonance production in the Sakai-Sugimoto model to the case of negative parity baryon resonances. Using holographic techniques we extract the generalized Dirac and Pauli baryon form factors as well as the helicity amplitudes for these baryonic states. Identifying the first negative parity resonance with the experimentally observed S_{11}(1535), we find reasonable agreement with experimental data from the JLab-CLAS collaboration. We also estimate the contribution of negative parity baryons to the proton structure functions.
We study baryons as Skyrmions in holographic QCD with D4/D8/D8-bar multi-D brane system in type IIA superstring theory, and also in the non-linear sigma model with hidden local symmetry (HLS). Comparing these two models, we find that the extra-dimension and its nontrivial curvature can largely change the role of (axial) vector mesons for baryons in four-dimensional space-time. In the HLS approach, the rho-meson field as a massive Yang-Mills field has a singular configuration in Skyrmion, which gives a strong repulsion for the baryon as a stabilizer. When a_1 meson is added in this approach, th…
We study on the spectrum and short-distance two-body force of holographic baryons by the matrix model, which is derived from Sakai-Sugimoto model in D0-D4 background (D0-D4/D8 system). The matrix model is derived by using the standard technique in string theory and it can describe multi-baryon system. We re-derive the action of the matrix model from open string theory on the wrapped baryon vertex, which is embedded in the D0- D4/D8 system. The matrix model offers a more systematic approach to the dynamics of the baryons at short distances. In our system, we find that the matrix model describe …
We discuss the mass gap in quantum Hall solitons (QHS) embedded in superstring theory. In particular, we give two holographic models which are obtained from D-brane configurations in type IIB superstring compactifications. The first one deals with the monolayered system in the D3/D7 brane set up. The second model corresponds to a multilayered system which is described by intersecting D5-branes wrapping a particular set of 3-cycles. In both models, we have shown that the mass gap is related to the filling factor.
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 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…
We study baryons in holographic QCD corresponding to 1+1 dimensional single-flavor ($N_f$=1) QCD for the first time. We formulate 1+1 QCD using an $S^1$-compactified D2/D8/$\overline{\rm D8}$ branes in the superstring theory, and describe the baryon as a topological configuration in 1+1 $N_f$=1 QCD, corresponding to $Π_1({\rm U(1)})={\bf Z}$. Unlike 1+3 QCD with $N_f \ge 2$, however, we find that the low-dimensional baryonic soliton is generally unstable against a scale transformation/variation and swells infinitely in 1+1 $N_f$=1 QCD at the leading of large $N_c$. We thus point out a serious …
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…
