The Chiral Model of Sakai-Sugimoto at Finite Baryon Density

In the context of holographic QCD we analyze Sakai-Sugimoto's chiral model at finite baryon density and zero temperature. The baryon number density is introduced through compact D4 wrapping S^4 at the tip of D8-\bar{D8}. Each baryon acts as a chiral point-like source distributed uniformly over R^3, and leads a non-vanishing U(1)_V potential on the brane. For fixed baryon charge density n_B we analyze the bulk energy density and pressure using the canonical formalism. The baryonic matter with point like sources is always in the spontaneously broken phase of chiral symmetry, whatever the density. The point-like nature of the sources and large N_c cause the matter to be repulsive as all baryon interactions are omega mediated. Through the induced DBI action on D8-\bar{D8}, we study the effects of the fixed baryon charge density n_B on the pion and vector meson masses and couplings. Issues related to vector dominance in matter in the context of holographic QCD are also discussed.Comment: V3: 39 pages, 16 figures, minor corrections, version to appear in JHEP. V2: references added, typos correcte

Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant

We compute the dimensionality dependence of $\eta/s$ for charged black branes with Gauss-Bonnet correction. We find that both causality and stability constrain the value of Gauss-Bonnet coupling constant to be bounded by 1/4 in the infinite dimensionality limit. We further show that higher dimensionality stabilize the gravitational perturbation. The stabilization of the perturbation in higher dimensional space-time is a straightforward consequence of the Gauss-Bonnet coupling constant bound.Comment: 16 pages,3 figures+3 tables,typos corrected, published versio

Stringy NJL and Gross-Neveu models at finite density and temperature

Nonlocal stringy versions of the Nambu-Jona-Lasinio and Gross-Neveu models arise in a certain limit of holographic QCD. We analyze the phase structure at finite density and temperature at strong coupling in terms of probe branes in the gravity dual. Comparison with the phase structure of the local field theory models shows qualitative agreement with some aspects, and disagreement with others. Finally, we explain how to construct the Landau potentials for these models by taking the probe branes off-shell.Comment: 32 pages, uses JHEP3.cls; v2, references added, version to be submitted to JHE

A Dual Geometry of the Hadron in Dense Matter

We identify the dual geometry of the hadron phase of dense nuclear matter and investigate the confinement/deconfinement phase transition. We suggest that the low temperature phase of the RN black hole with the full backreaction of the bulk gauge field is described by the zero mass limit of the RN black hole with hard wall. We calculated the density dependence of critical temperature and found that the phase diagram closes. We also study the density dependence of the rho meson mass.Comment: 16 pages, 4 figures, typos corrected, references adde

Cold Nuclear Matter In Holographic QCD

We study the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase characterized by a condensate of instantons on the probe D-branes in the string theory dual. As a result of electrostatic interactions between the instantons, this condensate expands towards the UV when the chemical potential is increased, giving a holographic version of the expansion of the Fermi surface. We argue based on properties of instantons that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density. This suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large N_c QCD at asymptotically large chemical potential. We study properties of the nuclear matter phase as a function of chemical potential beyond the transition and argue in particular that the model can be used to make a semi-quantitative prediction of the binding energy per nucleon for nuclear matter in ordinary QCD.Comment: 31 pages, LaTeX, 1 figure, v2: some formulae corrected, qualitative results unchange

Bulk Filling Branes and the Baryon Density in AdS/QCD with gravity back-reaction

We consider the gravity back reaction on the metric due to the baryon density in effective ads/qcd model by reconsidering the role of the charged AdS black hole. Previously it has been known that the U(1) charge is dual to the R-charge. Here we point out that if we consider the case where $AdS_5$ is completely filled with $N_f$ flavor branes, the gravity back reaction produces charged AdS black hole where the effect of charge on the metric is proportional to $N_f/N_c$. As a consequence, phase diagram changes qualitatively if we allow $N_f/N_c$ finite: it closes at the finite density unlike the probe brane embedding approach. Another issue we discuss here is the question whether there is any chemical potential dependence in the confining phase. We consider this problem in the hard wall model with baryon charge. We conclude that there is a non-trivial dependence on the chemical potential in this case also.Comment: 17 pages 3x2 figures, v2: references added;v3 published version, title change and reference adde

Holographic Nuclear Physics

We analyze the phases of the Sakai-Sugimoto model at finite temperature and baryon chemical potential. Baryonic matter is represented either by 4-branes in the 8-branes or by strings stretched from the 8-branes to the horizon. We find the explicit configurations and use them to determine the phase diagram and equation of state of the model. The 4-brane configuration (nuclear matter) is always preferred to the string configuration (quark matter), and the latter is also unstable to density fluctuations. In the deconfined phase the phase diagram has three regions corresponding to the vacuum, quark-gluon plasma, and nuclear matter, with a first-order and a second-order phase transition separating the phases. We find that for a large baryon number density, and at low temperatures, the dominant phase has broken chiral symmetry. This is in qualitative agreement with studies of QCD at high density.Comment: 27 pages, 26 figures. v2: Added a comment about higher derivative corrections to the DBI action in the smeared instanton in section 2.1. v3: References added, version published in JHEP. v4: misprints correcte

Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model

In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED anomaly. In the Sakai-Sugimoto model, which in a certain limit is dual to large-N_c QCD, we discuss the proper implementation of the QED axial anomaly, the (ambiguous) definition of chiral currents, and the calculation of the chiral magnetic effect. We show that this model correctly contains the so-called consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly. Introducing net chirality through an axial chemical potential, we find a nonvanishing vector current only before including this counterterm. This seems to imply the absence of the chiral magnetic effect in this model. On the other hand, for a conventional quark chemical potential and large magnetic field, which is of interest in the physics of compact stars, we obtain a nontrivial result for the axial current that is in agreement with previous calculations and known exact results for QCD.Comment: 35 pages, 4 figures, v2: added comments about frequency-dependent conductivity at the end of section 4; references added; version to appear in JHE

Criticality, Scaling and Chiral Symmetry Breaking in External Magnetic Field

We consider a D7-brane probe of $AdS_{5}\times S^5$ in the presence of pure gauge $B$-field. The dual gauge theory is flavored Yang-Mills theory in external magnetic field. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and study the discrete self-similar behavior of the theory near the origin of the parametric space. We calculate the critical exponents of the bare quark mass and the fermionic condensate. A study of the meson spectrum supports the expectation based on thermodynamic considerations that at zero bare quark mass the stable phase of the theory is a chiral symmetry breaking one. Our study reveals the self-similar structure of the spectrum near the critical phase of the theory, characterized by zero fermionic condensate and we calculate the corresponding critical exponent of the meson spectrum.Comment: 29 pages, 9 figures. Accepted in JHEP. Updated to mach the published version. One figure added, some definitions improve