Complexity and phase transitions in a holographic QCD model

Applying the "Complexity=Action" conjecture, we study the holographic complexity close to crossover/phase transition in a holographic QCD model proposed by Gubser et al. This model can realize three types of phase transition, crossover or first and second order, depending on the parameters of the dilaton potential. The re-scaled late-time growth rate of holographic complexity density for the three cases is calculated. Our results show that it experiences a fast drop/jump close to the critical point while approaching constants far beyond the critical temperature. Moreover, close to the critical temperature, it shows a behavior characterizing the type of the transition. These features suggest that the growth rate of the holographic complexity may be used as a good parameter to characterize the phase transition. The Lloyd's bound is always satisfied for the cases we considered but only saturated for the conformal case.Comment: v1: 14 pages, 2 figures; v2: refs added, minor modifications. arXiv admin note: substantial text overlap with arXiv:1608.03072; v3: More details on the Lloyd's bound, matching the published versio

Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems

We investigate the behavior of entanglement entropy in the holographic QCD model proposed by Gubser et al. By choosing suitable parameters of the scalar self-interaction potential, this model can exhibit various types of phase structures: crossover, first order and second order phase transitions. We use entanglement entropy to probe the crossover/phase transition, and find that it drops quickly/suddenly when the temperature approaches the critical point which can be seen as a signal of confinement. Moreover, the critical behavior of the entanglement entropy suggests that we may use it to characterize the corresponding phase structures.Comment: v1:19 pages, 5 figures; v2: refs added; v3: 20 pages, high-temperature behaviors of holographic entanglement entropy are given, accecpted for publication by NP

Holographic Thermalization in Charged Dilaton Anti-de Sitter Spacetime

We study holographic thermalization in spacetimes with a chemical potential and a non-trivial dilaton field. Three non-local observables are used to probe the whole process and investigate the effect of the ratio of the chemical potential over temperature $\chi$ and the dilaton-Maxwell coupling constant $\alpha$. It is found that the saturation time is not always a monotonically increasing function of $\chi$, the situation depends on $\alpha$. When $0 \leq\alpha \leq 1$, larger $\chi$ yields longer saturation time, while for $\alpha>1$, the situation becomes more complex. More interesting, we found that although $\alpha$ indeed has influence on the whole thermalization process, it nearly does not affect the saturation time, which indicates the universality of the saturation time for the dual one-parameter field theories.Comment: 22 pages, 5 figure

Charged Scalar Perturbations around Garfinkle-Horowitz-Strominger Black Holes

We examine the stability of the Garfinkle-Horowitz-Strominger (GHS) black hole under charged scalar perturbations. We find that different from the neutral scalar field perturbations, only two numerical methods, such as the continued fraction method and the asymptotic iteration method, can keep high efficiency and accuracy requirements in the frequency domain computations. The comparisons of the efficiency between these two methods have also been done. Employing the appropriate numerical method, we show that the GHS black hole is always stable against charged scalar perturbations. This is different from the result obtained in the de Sitter and Anti-de Sitter black holes. Furthermore we argue that in the GHS black hole background there is no amplification of the incident charged scalar wave to cause the superradiance, so that the superradiant instability cannot exist in this spacetime.Comment: 24 pages, 5 figure

SL(2,C) gravity on noncommutative space with Poisson structure

The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.Comment: 12 pages, no figures; v2: 13 pages, clarifications and references added; v3: clarifications added; v4: more clarifications and references added, final version to appear in Phys. Rev.

Superradiant instability of Kerr-de Sitter black holes in scalar-tensor theory

We investigate in detail the mechanism of superradiance to render the instability of Kerr-de Sitter black holes in scalar-tensor gravity. Our results provide more clues to examine the scalar-tensor gravity in the astrophysical black holes in the universe with cosmological constant. We also discuss the spontaneous scalarization in the de Sitter background and find that this instability can also happen in the spherical de Sitter configuration in a special style.Comment: (v2)21 pages, 21 figures; Sec. V revised; This version has been accepted for publication by JHE