We present new anisotropic black brane solutions in 5D Einstein-dilaton-two-Maxwell system. The anisotropic background is specified by an arbitrary dynamical exponentν, 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 toν= 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 (μ_ϑ,b, T_ϑ,b) depending on the orientationϑof quark-antiquark pairs in respect to the heavy ions collision line.

We explore a possibility for the Universe to cross the $w=-1$ cosmological constant barrier for the dark energy state parameter. We consider the Universe as a slowly decaying D3-brane. The D3-brane dynamics are approximately described by a nonlocal string tachyon interaction and the backreaction of gravity is incorporated in the closed string tachyon dynamics. In a local effective approximation this model contains one phantom component and one usual field with a simple polynomial interaction. To understand cosmological properties of this system we study toy models with the same scalar fields but with modified interactions. These modifications admit polynomial superpotentials. We find restrictions on these interactions under which it is possible to reach $w=-1$ from below at large time. Explicit solutions with the dark energy state parameter crossing or not crossing the barrier $w=-1$ at large time are presented.

We study the evolution of holographic complexity of pure and mixed states in 1 + 1-dimensional conformal field theory following a local quench using both the “complexity equals volume” (CV) and the “complexity equals action” (CA) conjectures. We compare the complexity evolution to the evolution of entanglement entropy and entanglement density, discuss the Lloyd computational bound and demonstrate its saturation in certain regimes. We argue that the conjectured holographic complexities exhibit some non-trivial features indicating that they capture important properties of what is expected to be effective (or physical) complexity.

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 ℓ is increasing for all ℓ in the isotropic case (in regions of (μ, 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 are based 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 μ. 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.