We study dense nuclear and quark matter within a single microscopic approach, namely the holographic Sakai-Sugimoto model. Nuclear matter is described via instantons in the bulk, and we show that instanton interactions are crucial for a continuous connection of chirally broken and chirally symmetric phases. The continuous path from nuclear to quark matter includes metastable and unstable stationary points of the potential, while the actual chiral phase transition remains of first order, as in earlier approximations. We show that the model parameters can be chosen to reproduce low-density properties of nuclear matter and observe a non-monotonic behavior of the speed of sound as a function of the baryon chemical potential, as suggested by constraints from QCD and astrophysics.

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Contents 1 Introduction 1 2 Geometry 3 3 Deformed instantons and thermodynamic quantities 4 4 Results 9 4.1 Phase diagram 9 4.2 Connecting nuclear matter with quark matter at finite temperature 12 4.3 Speed of sound 13 5 Summery 16 A Interaction profile of parameter 17 B Phase diagram for Non-interaction case 17We 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 critical chemical potential has been changed from baryon to quark. In our results, this point is non-physical also, see continuity between the baryonic and quark phases. Speed of sound at the low chemical potential in the presence of temperature is different, but when the potential increases, the effect of temperature on the speed of sound will remain unchanged. In the phase diagram, for significant chemical potential, chiral symmetry is restored and provides all things that we have the realistic model.