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Register a new userHolographic Anisotropic Background with Confinement-Deconfinement Phase Transition
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We present new anisotropic black brane solutions in 5D Einstein-dilaton-two-Maxwell system. The anisotropic background is specified by an arbitrary dynamical exponent $ u$, a nontrivial warp factor, a non-zero dilaton field, a non-zero time component of the first Maxwell field and a non-zero longitudinal magnetic component of the second Maxwell field. The blackening function supports the Van der Waals-like phase transition between small and large black holes for a suitable first Maxwell field charge. The isotropic case corresponding to $ u = 1$ and zero magnetic field reproduces previously known solutions. We investigate the anisotropy influence on the thermodynamic properties of our background, in particular, on the small/large black holes phase transition diagram. We discuss applications of the model to the bottom-up holographic QCD. The RG flow interpolates between the UV section with two suppressed transversal coordinates and the IR section with the suppressed time and longitudinal coordinates due to anisotropic character of our solution. We study the temporal Wilson loops, extended in longitudinal and transversal directions, by calculating the minimal surfaces of the corresponding probing open string world-sheet in anisotropic backgrounds with various temperatures and chemical potentials. We find that dynamical wall locations depend on the orientation of the quark pairs, that gives a crossover transition line between confinement/deconfinement phases in the dual gauge theory. Instability of the background leads to the appearance of the critical points $(mu_{vartheta,b}, T_{vartheta,b})$ depending on the orientation $vartheta$ of quark-antiquark pairs in respect to the heavy ions collision line.
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We discuss a general five-dimensional completely anisotropic holographic model with three different spatial scale factors, characterized by a Van der Waals-like phase transition between small and large black holes. A peculiar feature of the model is the relation between anisotropy of the background and anisotropy of the colliding heavy ions geometry. We calculate the holographic entanglement entropy (HEE) of the slab-shaped region, the orientation of which relatively to the beams line and the impact parameter is characterized by the Euler angles. We study the dependences of the HEE and its density on the thermodynamic (temperature, chemical potential) and geometric (parameters of anisotropy, thickness, and orientation of entangled regions) parameters. As a particular case the model with two equal transversal scaling factors is considered. This model is supported by the dilaton and two Maxwell fields. In this case we discuss the HEE and its density in detail: interesting features of this model are jumps of the entanglement entropy and its density near the line of the small/large black hole phase transition. These jumps depend on the anisotropy parameter, chemical potential, and orientation. We also discuss different definitions and behavior of c-functions in this model. The c-function calculated in the Einstein frame decreases while increasing $ell$ for all $ell$ in the isotropic case (in regions of $(mu,T)$-plane far away from the line of the phase transition). We find the non-monotonicity of the c-functions for several anisotropic configurations, which however does not contradict with any of the existing c-theorems since they all base on Lorentz invariance.
We present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action. This model generalizing isotropic holographic model with light quarks is characterized by a Van der Waals-like phase transition between small and large black holes. We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane -- temperature $T$ and chemical potential $mu$. The Cornell potential behavior in this anisotropic model is also studied. The asymptotics of the Cornell potential at large distances strongly depend on the parameter of anisotropy and orientation. There is also a nontrivial dependence of the Cornell potential on the boundary conditions of the dilaton field and parameter of anisotropy. With the help of the boundary conditions for the dilaton field one fits the results of the lattice calculations for the string tension as a function of temperature in isotropic case and then generalize to the anisotropic one.
We study the T-{mu} phase diagram of anisotropic media, created in heavy-ion collisions (HIC). Such a statement of the problem is due to several indications that this media is anisotropic just after HIC. To study T-{mu} phase diagram we use holographic methods. To take into account the anisotropy we use an anisotropic black brane solutions for a bottom-up QCD approach in 5-dim Einstein-dilaton-two-Maxwell model constructed in our previous work. We calculate the minimal surfaces of the corresponding probing open string world-sheet in anisotropic backgrounds with various temperatures and chemical potentials. The dynamical wall (DW) locations, providing the quark confinement, depend on the orientation of the quark pairs, that gives a crossover transition between confinement/deconfinement phases in the dual gauge theory.
Recently Herzog has shown that deconfinement of AdS/QCD can be realized, in the hard-wall model where the small radius region is removed in the asymptotically AdS space, via a first order Hawking-Page phase transition between a low temperature phase given by a pure AdS geometry and a high temperature phase given by the AdS black hole in Poincare coordinates. In this paper we first extend Herzogs work to the hard wall AdS/QCD model in curved spaces by studying the thermodynamics of AdS black holes with spherical or negative constant curvature horizon, dual to a non-supersymmetric Yang-Mills theory on a sphere or hyperboloid respectively. For the spherical horizon case, we find that the temperature of the phase transition increases by introducing an infrared cutoff, compared to the case without the cutoff; For the hyperbolic horizon case, there is a gap for the infrared cutoff, below which the Hawking-Page phase transition does not occur. We also discuss charged AdS black holes in the grand canonical ensemble, corresponding to a Yang-Mills theory at finite chemical potential, and find that there is always a gap for the infrared cutoff due to the existence of a minimal horizon for the charged AdS black holes with any horizon topology.
In the framework of a holographic QCD approach we study an influence of matters on the deconfinement temperature, $T_c$. We first consider quark flavor number ($N_f$) dependence of $T_c$. We observe that $T_c$ decreases with $N_f$, which is consistent with a lattice QCD result. We also delve into how the quark number density $rho_q$ affects the value of $T_c$. We find that $T_c$ drops with increasing $rho_q$. In both cases, we confirm that the contributions from quarks are suppressed by $1/N_c$, as it should be, compared to the ones from a gravitational action (pure Yang-Mills).
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