Quantum chromodynamics is notoriously difficult to solve at nonzero baryon density, and most models or effective theories of dense quark or nuclear matter are restricted to a particular density regime and/or a particular form of matter. Here we study dense (and mostly cold) matter within the holographic Sakai-Sugimoto model, aiming at a strong-coupling framework in the wide density range between nuclear saturation density and ultra-high quark matter densities. The model contains only three parameters, and we ask whether it fulfills two basic requirements of real-world cold and dense matter, a first-order onset of nuclear matter and a chiral phase transition at high density to quark matter. Such a model would be extremely useful for astrophysical applications because it would provide a single equation of state for all densities relevant in a compact star. Our calculations are based on two approximations for baryonic matter, firstly an instanton gas and secondly a homogeneous ansatz for the non-abelian gauge fields on the flavor branes of the model. While the instanton gas shows chiral restoration at high densities but an unrealistic second-order baryon onset, the homogeneous ansatz behaves exactly the other way around. Our study thus provides all ingredients that are necessary for a more realistic model and allows for systematic improvements of the applied approximations.Comment: 31 pages, 7 figures, v2: references added, version to appear in Physical Review

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 multibaryon 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 stable baryonic states only if ζ = Uis related to the number density of smeared D0-branes. This result in our paper is exactly the same as some previous presented results studied on this system as [27]. We also compute the baryon spectrum (k = 1 case) and short-distance two-body force of baryons (k = 2 case). The baryon spectrum is modified and could be able to fit the experimental data if we choose suitable value for ζ. And the short-distance two-body force of baryons is also modified by the appearance of smeared D0-branes from the original Sakai-Sugimoto model. If ζ > 2, we find that the baryon spectrum would be totally complex and an attractive force will appear in the short-distance interaction of baryons, which may consistently correspond to the existence of unstable baryonic states.

We extend the holographic analysis of light-baryon spectrum in [50] to the case involving the heavy flavors. With the construction of the Witten-Sakai-Sugimoto model in the D0-D4 background, we use the mechanism proposed in [59,60,61] by including two light and one heavy flavor branes, to describe the heavy-light baryons as heavy mesons bound to a flavor instanton. The background geometry of this model corresponds to an excited state in the dual field theory with nonzero glue condensate TrF ∧ F = 8π 2 N cκ , or equivalently a θ angle, which is proportional to the number density of the D0-brane charge. At strongly coupled limit, this model shows that the heavy meson is always bound in the form of the zero mode of the flavor instanton in the fundamental representation. We systematically study the quantization for the effective Lagrangian of heavy-light baryons by employing the soliton picture, and derive the mass spectrum of heavy-light baryons in the situation with singleand double-heavy baryon. We find the difference in the mass spectrum becomes smaller if the density of D0-brane charge increases and the constraint of stable states of the heavylight baryons is 1 < b < 3. It indicates that baryon can not stably exist for sufficiently large density of D0 charge which is in agreement with the conclusions in the previous study of this model.

We construct the gravitational solution of the Witten-Sakai-Sugimoto model by introducing a magnetic field on the flavor brane. With taking into account their backreaction, we re-solve the type IIA supergravity in the presence of the magnetic field. Our calculation shows the gravitational solutions are magnetic-dependent and analytic both in the bubble (confined) and black brane (deconfined) case. We study the dual field theory at the leading order in the ratio of the number of flavors and colors, also in the Veneziano limit. Some physical properties related to the hadronic physics in an external magnetic field are discussed by using our confined backreaction solution holographically. We also investigate the thermodynamics and holographic renormalization of this model in both phases by our solution. Since the backreaction of the magnetic field is considered in our gravitational solution, it allows us to study the Hawking-Page transition with flavors and colors of this model in the presence of the magnetic field. Finally we therefore obtain the holographic phase diagram with the contributions from the flavors and the magnetic field. Our holographic phase diagram is in agreement with lattice QCD result qualitatively, which thus can be interpreted as the inhibition of confinement or chirally broken symmetry by the magnetic field. 1 the behavior of the Witten-Sakai-Sugimoto model interpolates between NJL and QCD according to [15,30,31,32,33].

This is an extensive work to our previous paper [8] studied on the D0-D4/D8 holographic system. We compute the three-body force for baryons with the D0-D4/D8 matrix model derived in [8] with considering the non-zero QCD vacuum. We obtain the three-body force at short distances but modified by the appearance of the smeared D0-branes i.e. considering the effects from the non-trivial QCD vacuum. We firstly test our matrix model in the case of 't Hooft instanton and then in two more realistic case:(1) three-neutrons with averaged spins and (2) proton-proton-neutron (or proton-neutron-proton). The three-body potential vanishes in the former case while in two latter cases it is positive i.e. repulsive and makes sense only if the constraint for stable baryonic state is satisfied. We require all the baryons in our computation aligned on a line. These may indicate that the cases in dense states of neutrons such as in neutron stars, Helium-3 or Tritium nucleus all with the non-trivial QCD vacuum. 1