Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces

Based on the principle of reparametrization invariance, the general structure of physically relevant classical matter systems is illuminated within the Lagrangian framework. In a straightforward way, the matter Lagrangian contains background interaction fields, such as a 1-form field analogous to the electromagnetic vector potential and symmetric tensor for gravity. The geometric justification of the interaction field Lagrangians for the electromagnetic and gravitational interactions are emphasized. The generalization to E-dimensional extended objects (p-branes) embedded in a bulk space M is also discussed within the light of some familiar examples. The concept of fictitious accelerations due to un-proper time parametrization is introduced, and its implications are discussed. The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. The simplest model with such fields is analyzed and its relevance to dark matter and dark energy phenomena on large/cosmological scales is inferred. Unusual pathological behavior in the Newtonian limit is suggested to be a precursor of quantum effects and of inflation-like processes at microscopic scales.

Evolution of Growth Density Equation by Constraints on Effective Newtonian Constant Geff

The acceleration of the universe is described as a consequence of the extrinsic curvature of the space-time embedded in a bulk space, defined by the Einstein-Hilbert. Using the linear approximation of Nash-Green theorem, we obtain the related perturbed equations in which just the gravitational-tensor field equations contribute to propagation of cosmological perturbations. In accordance with Big Bang Nucleosynthesis and solar constraints, we calculate numerically the effective Newtonian function Geff to constrain the related parameters of the model. We numerically solve the growth density equation for two possible family of solutions leading to an interesting overdensity and, in some cases, a mild damping of the growth profiles, with a top amplification of the growth perturbations around 14% in comparison with LCDM model and quintessence. The effective gravitational Phi and Newtonian curvature Psi are also analysed showing mild perturbations in early times induced only by the extrinsic curvature differently from the LambdaCDM standards.

Holography and criticality in matchgate tensor networks

The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand these bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1 + 1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, obtaining highly accurate critical data. Within our framework, we also produce translation-invariant critical states by an efficiently contractible tensor network with the geometry of the multiscale entanglement renormalization ansatz. Furthermore, we establish a link between holographic quantum error–correcting codes and tensor networks. This work is expected to stimulate a more comprehensive study of tensor network models capturing bulk-boundary correspondences.

Vacuum Constraints for Realistic Strongly Coupled Heterotic M-Theories

The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific S U ( 4 ) vector bundle leading to the “heterotic standard model” in the observable sector. A generic formalism for a consistent hidden sector gauge bundle, within the context of strongly coupled heterotic M-theory, is presented. Anomaly cancellation and the associated bulk space 5-branes are discussed in this context. The further compactification to a 4-dimensional effective field theory on a linearized BPS double domain wall is then presented to order κ 11 4 / 3 . Specifically, the generic constraints required for anomaly cancellation and by the linearized domain wall solution, restrictions imposed by the vanishing of the D-terms and, finally, the constraints imposed by the necessity for positive, perturbative squared gauge couplings to this order are presented in detail.

Dynamical Codimension – 2 Brane in a Warped Six Dimensional Space-time

In this paper we present the Einstein equation extended in six-dimensions (6D) from the formation of codimension-2 brane, which is created by a 4-brane and 4-anti brane moving in the warped 6D “bulk” space-time. The system of equations of motion for the dynamical codimension - 2 brane has been derived to describe the cosmological evolution on the probe branes. Some cosmological consequences are investigated.

A bulk localized state and new holographic renormalization group flow in 3D spin-3 gravity

We construct a localized state of a scalar field in 3D spin-3 gravity. 3D spin-3 gravity is thought to be holographically dual to [Formula: see text]-extended CFT on a boundary at infinity. It is known that while [Formula: see text] algebra is a nonlinear algebra, in the limit of large central charge [Formula: see text] a linear finite-dimensional subalgebra generated by [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] is singled out. The localized state is constructed in terms of these generators. To write down an equation of motion for a scalar field which is satisfied by this localized state, it is necessary to introduce new variables for an internal space [Formula: see text], [Formula: see text], [Formula: see text], in addition to ordinary coordinates [Formula: see text] and [Formula: see text]. The higher-dimensional space, which combines the bulk space–time with the “internal space,” which is an analog of superspace in supersymmetric theory, is introduced. The “physical bulk space–time” is a 3D hypersurface with constant [Formula: see text], [Formula: see text] and [Formula: see text] embedded in this space. We will work in Poincaré coordinates of AdS space and consider [Formula: see text]-quasi-primary operators [Formula: see text] with a conformal weight [Formula: see text] in the boundary and study two and three point functions of [Formula: see text]-quasi-primary operators transformed as [Formula: see text]. Here, [Formula: see text] and [Formula: see text] are [Formula: see text] generators in the hyperbolic basis for Poincaré coordinates. It is shown that in the [Formula: see text] limit, the conformal weight changes to a new value [Formula: see text]. This may be regarded as a Renormalization Group (RG) flow. It is argued that this RG flow will be triggered by terms [Formula: see text] added to the action.

On Quasinormal Modes for Scalar Perturbations of Static Spherically Symmetric Black Holes in Nash Embedding Framework

In this paper we investigate scalar perturbations of black holes embedded in a five-dimensional bulk space. The quasinormal frequencies of such black holes are calculated using the third order of Wentzel, Kramers, and Brillouin (WKB) approximation for scalar perturbations. The high overtones of quasinormal modes indicate a resonant-like set of black holes suggesting a serious constraint of embedding models in five dimensions.

Covariant extrinsic gravity and the geometric origin of dark energy

In this paper, we construct the covariant or model independent induced Einstein–Yang–Mills field equations on a four-dimensional brane embedded isometrically in an D-dimensional bulk space, assuming the matter fields are confined to the brane. Applying this formalism to cosmology, we derive the generalized Friedmann equations. We derive the density parameter of dark energy in terms of width of the brane, normal curvature radii and the number of extra large dimensions. We show that dark energy could actually be the manifestation of the local extrinsic shape of the brane. It is shown that the predictions of this model are in good agreement with observation if we consider an 11-dimensional bulk space.

RG FLOW OF TRANSPORT QUANTITIES

The RG flow equation of various transport quantities are studied in arbitrary space–time dimensions, in the fixed as well as fluctuating background geometry both for the Maxwellian and DBI type of actions. The regularity condition on the flow equation of the conductivity at the horizon for the DBI action reproduces naturally the leading order result of Hartnoll et al. [J. High Energy Phys. 04, 120 (2010)]. Motivated by the result of van der Marel et al. [Science 425, 271 (2003], we studied, analytically, the conductivity versus frequency plane by dividing it into three distinct parts: ω < T, ω > T and ω ≫ T. In order to compare, we choose (3+1)-dimensional bulk space–time for the computation of the conductivity. In the ω < T range, the conductivity does not show up the Drude like form in any space–time dimensions. In the ω > T range and staying away from the horizon, for the DBI action with unit dynamical exponent, nonzero magnetic field and charge density, the conductivity goes as ω-2/3, whereas the phase of the conductivity, goes as, arctan ( Im σxx/ Re σxx) = π/6 and arctan ( Im σxy/ Re σxy) = -π/3. There exists a universal quantity at the horizon that is the phase angle of conductivity, which either vanishes or an integral multiple of π. Furthermore, we calculate the temperature dependence to the thermoelectric and the thermal conductivity at the horizon. The charge diffusion constant for the DBI action is studied.