Abstract:We develop the boundary derivative expansion (BDE) formalism of fluid/gravity correspondence to nonconformal version through the compactified, nearextremal black D4-brane. We offer an explicit calculation of 9 second order transport coefficients, i.e., the τ π , τ * π , τ Π , λ 1,2,3 and ξ 1,2,3 for the strongly coupled, uncharged and nonconformal relativistic fluid which is the holographic dual of compactified, near extremal black D4-brane. We also show that the nonconformal fluid considered in this work is free of causal problem and admits the Haack-Yarom relation 4λ 1 − λ 2 = 2ητ π .
We develop the framework of boundary derivative expansion (BDE) formalism of fluid/gravity correspondence in compactified D4-brane system, which is a nonconformal background used in top-down holographic QCD models. Such models contain the D4-D6 model and the Sakai-Sugimoto (SS) model, with the background of the compactified black D4 branes under the near horizon limit. By using the dimensional reduction technique, we derive a 5D Einstein gravity minimally coupled with 3 scalar fields from the 10D D4-brane background. Following the BDE formalism of fluid/gravity correspondence in the conformal background, we directly derive all the first order transport coefficients for nonconformal gluonic matter. The results of the ratio of the bulk to shear viscosity and the sound speed agree with those obtained from the Green-Kubo method. This agreement guarantees the validity of the BDE formalism of fluid/gravity duality in the nonconformal D-brane background, which can be used to calculate the second order transport coefficients in nonconformal background.
We investigate the baryon number susceptibilities up to fourth order along different freeze-out lines in a holographic QCD model with the critical end point (CEP), and we propose that the peaked baryon number susceptibilities along the freeze-out line can be used as a clean signature to locate the CEP in the QCD phase diagram. On the temperature and baryon chemical potential plane, the ratio of the baryon number susceptibilities (up to fourth order) forms a ridge along the phase boundary, and develops a sword shape mountain standing upright around the CEP in a narrow and oblate region. This feature is model independent and universal if the CEP exists. The measurement of baryon number susceptibilities from heavy-ion collision experiment is along the freeze-out line. If the freeze-out line crosses the foot of the CEP mountain, then one can observe the peaked baryon number susceptibilities along the freeze-out line, and the kurtosis of the baryon number distributions has the tallest magnitude. The data from the first phase of beam energy scan program at the Relativistic Heavy Ion Collisions indicates that a peak of the kurtosis of the baryon number distribution would show up at the collision energy around 5 GeV, which suggests that the freeze-out line crosses the foot of the CEP mountain and the summit of the CEP would be located nearby around the collision energy of 3 GeV. PACS numbers: 13.40.-f, 25.75.-q, 11.10.WxQuantum Chromodynamics (QCD) is the fundamental theory of the strong interactions. The QCD vacuum structure and its phase diagram under extreme conditions has been always one of the most attractive topics to understand the nonperturbative nature of the strong interactions. In the QCD vacuum, the chiral symmetry is spontaneously broken and color-charged quarks and gluons are confined. It is expected that at high temperature and/or baryon density, the system undergoes a phase transition from hadronic phase to chiral restored and deconfined quark-gluon phase. In the case of physical quark masses, QCD chiral models as well as lattice QCD predicted that the phase transition is of smooth crossover at small baryon chemical potentia and high temperature [1]. Due to the sign problem, it is still quite challenging for lattice QCD simulation to work at finite baryon chemical potential. However, through symmetry classes analysis [2, 3] and effective model predictions [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], it has been generally believed that QCD phase transition is of first order at high baryon chemical potential, and the end point of the first order phase transition line toward the crossover region is called the critical end point (CEP). For theoretical review of QCD phase diagram and the CEP, please refer to Refs. [22, 23] and references therein. Different models such as Nambu-Jona-Lasinio (NJL) model, the Polyakov-loop improved NJL (PNJL) model, linear sigma model, quark-meson (QM) model, the Polyakov-loop improved QM model, and the Dyson-Schwinger equations (DSE) give various location ...
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