Abstract
A preliminary quantitative study to match the lattice QCD simulation on the chiral and deconfining phase transitions of QCD in the bottom-up holographic framework is given. We constrain the relation between dilaton field ϕ and metric warp factor Ae and get several reasonable models in the Einstein-Dilaton system. Using the potential reconstruction approach, we solve the corresponding gravity background. Then we fit the background-related parameters by comparing the equation of state with the two-flavor lattice QCD results. After that we study the temperature dependent behavior of Polyakov loop and chiral condensate under those background solutions. We find that the results are in good agreement with the two-flavor lattice results. All the studies about the equation of state, the Polyakov loop and the chiral condensate signal crossover behavior of the phase transitions, which are consistent with the current understanding on the QCD phase transitions with physical quark mass. Furthermore, the extracted transition temperatures are comparable with the two-flavor lattice QCD results.
Highlights
Based on theoretical consideration and lattice QCD simulation [2,3,4], a possible 2 + 1 flavor phase diagram in the current quark mass plane is summarized in the sketch shown in Fig.1 [2]
All the studies about the equation of state, the Polyakov loop and the chiral condensate signal crossover behavior of the phase transitions, which is consistent with the current understanding on the QCD phase transitions with physical quark mass
It is noted that in the region of two light flavors where mu = md ≃ O(MeV) and ms = ∞, even very small quark mass would drive the second-order transition in the chiral limit to a crossover transition with finite quark mass (in analogy to the O(4) σ model [5] noting that SU (2)L × SU (2)R ≃ O(4))
Summary
In bottom-up holographic studies, the deconfining phase transition has already been widely investigated in the Einstein-dilaton system [60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76]. In [60, 61, 67], the authors tried to study thermodynamics of QCD with flavors in the Einstein-dilaton system Following this logic and as a preliminary try, we will solve the Einstein-dilaton action Sb as the geometrical background and take the matter action Sm as a probe, which should be considered as an approximation of the full system. We consider chiral and deconfining phase transitions in the two-flavor case (Nf = 2), so the background geometry will be constrained by Nf = 2 thermodynamics before studying the temperature dependent behavior of chiral condensate and Polyakov loop. We will first outline the necessary framework of the Einstein-dilaton system, and try to constrain the background and give several models for study
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