Higher Dimensional Background Research Articles

Holographic entanglement entropy with Power-Maxwell electrodynamics in higher dimensional AdS black hole spacetime* *Supported by the National Natural Science Foundation of China (11665015), the Guizhou Provincial Science and Technology Planning Project of China (qiankehejichu-ZK[2021]yiban026), and the Guizhou Province ordinary institutions of higher learning top science and technology talents Support plan of China (qianjiaoheKY[2019]062).

We investigate the behaviors of the scalar operator and holographic entanglement entropy in the metal/superconductor phase transition with Power-Maxwell electrodynamics in a higher dimensional background away from the probe limit. We observe that the larger parameters b and q make the condensation of the scalar operator more difficult, and the critical temperature decreases more slowly as the factors increase. In the belt geometry, the value of the entanglement entropy in the metal and superconductor phases is not only related to the the strength of the Power-Maxwell field but also to the width of the strip geometry. At the phase transition point, the discontinuous slope of entanglement entropy is universal for different model factors. It turns out that holographic entanglement entropy is a powerful tool to probe the properties of the phase transition in this holographic superconductor model.

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer k. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index k of the background black hole metric, which shows that a larger k makes it harder for the condensation to form. We also observe that the index k affects the conductivity and the gap frequency of the holographic superconductors.

Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress–energy tensor

We provide irreducible expressions for the metric variations of the gravitational action terms constructed from the 17 curvature invariants of order six in the derivatives of the metric tensor, i.e., from the geometrical terms appearing in the diagonal heat-kernel or Gilkey–DeWitt coefficient a3. We then express, for a four-dimensional spacetime, the approximated stress–energy tensor constructed from the renormalized DeWitt–Schwinger effective action associated with a massive scalar field. We also construct, for higher dimensional spacetimes, the infinite counterterms of order six in the derivatives of the metric tensor appearing on the left-hand side of Einstein equations as well as the contribution associated with the cubic Lovelock gravitational action. In the appendix, we provide a list of geometrical relations we have used and which are more generally helpful for calculations in two-loop quantum gravity in a four-dimensional background or for calculations in one-loop quantum gravity in higher dimensional background. We also obtain the approximated stress–energy tensors associated with a massive spinor field and a massive vector field propagating in a four-dimensional background.

Poly-Essential and General Hyperelastic World (Brane) Models

This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient type describable as hyperelastic, for which a complete set of equations of motion is provided just by the energy-momentum conservation law. Particular cases include those of a perfect fluid in quintessential backgrounds of various kinds, as well as models of the elastic solid kind that has been proposed to account for cosmic acceleration. It is shown how an appropriately generalised Hadamard operator can be used to construct a symplectic structure that controles the evolution of small perturbations, and that provides a characteristic equation governing the propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds. The special case of a poly-essential model—the k-essential analogue of an ordinary polytropic fluid—is examined and shown to be well behaved (like the fluid) only if the pressure to density ratio w is positive.

Primordial magnetic seed fields from extra dimensions

Dynamical extra dimensions break the conformal invariance of Maxwell's equations in four dimensions. A higher-dimensional background with n contracting extra dimensions and four expanding dimensions is matched to an effectively four-dimensional standard radiation dominated universe. The resulting spectrum for the magnetic field is calculated taking into account also the momenta along the extra dimensions. Imposing constraints from observations an upper limit on the strength of magnetic seed fields is found. Depending on the number of extra dimensions, cosmologically interesting magnetic fields can be created.

Essentials of classical brane dynamics

This paper provides a self-contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined to a worldsheet of the corresponding dimension (respectively one, two, and three) in a thin limit approximation in an ordinary 4-dimensional spacetime background. This category also includes “brane world” models that treat the observed universe as a 3-brane in 5 or higher dimensional background. The first sections are concerned with purely kinematic aspects: it is shown how, to second differential order, the geometry (and in particular the inner and outer curvature) of a brane worldsheet of arbitrary dimension is describable in terms of the first, second, and third fundamental tensor. The later sections show how—to lowest order in the thin limit—the evolution of such a brane worldsheet will always be governed by a simple tensorial equation of motion whose left hand side is the contraction of the relevant surface stress tensor T¯µv with the (geometrically defined) second fundamental tensor Kμνρ, while the right hand side will simply vanish in the case of free motion and will otherwise be just the orthogonal projection of any external force density that may happen to act on the brane.