Supergravity, Non-Conformal Field Theories and Brane-Worlds

We consider the supergravity dual descriptions of non-conformal super Yang-Mills theories realized on the world-volume of Dp-branes. We use the dual description to compute stress-energy tensor and current correlators. We apply the results to the study of dilatonic brane-worlds described by non-conformal field theories coupled to gravity. We find that brane-worlds based on D4 and D5 branes exhibit a localization of gauge and gravitational fields. We calculate the corrections to the Newton and Coulomb laws in these theories.Comment: 24 pages, Latex, 2 figure

Simple quantum cosmology: Vacuum energy and initial state

A static non-singular 10-dimensional closed Friedmann universe of Planck size, filled with a perfect fluid with an equation of state with w = -2/3, can arise spontaneously by a quantum fluctuation from nothing in 11-dimensional spacetime. A quantum transition from this state can initiate the inflationary quantum cosmology outlined in Ref. 2 [General Relativity and Gravitation 33, 1415, 2001 - gr-qc/0103021]. With no fine-tuning, that cosmology predicts about 60 e-folds of inflation and a vacuum energy density depending only on the number of extra space dimensions (seven), G, h, c and the ratio between the strength of gravity and the strength of the strong force. The fraction of the total energy in the universe represented by this vacuum energy depends on the Hubble constant. Hubble constant estimates from WMAP, SDSS, the Hubble Key Project and Sunyaev-Zeldovich and X-ray flux measurements range from 60 to 72 km/(Mpc sec). With a mid-range Hubble constant of 65 km/(Mpc sec), the model in Ref. 2 predicts Omega-sub-Lambda = 0.7Comment: To be published in General Relativity and Gravitation, Vol. 37, May 2005. 5 pages, no figure

Equivalence Between Space-Time-Matter and Brane-World Theories

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let

Gauge-Dependent Cosmological "Constant"

When the cosmological constant of spacetime is derived from the 5D induced-matter theory of gravity, we show that a simple gauge transformation changes it to a variable measure of the vacuum which is infinite at the big bang and decays to an astrophysically-acceptable value at late epochs. We outline implications of this for cosmology and galaxy formation.Comment: 14 pages, no figures, expanded version to be published in Class. Quantum Gra

Moduli-Space Approximation for BPS Brane-Worlds

We develop the moduli-space approximation for the low energy regime of BPS-branes with a bulk scalar field to obtain an effective four-dimensional action describing the system. An arbitrary BPS potential is used and account is taken of the presence of matter in the branes and small supersymmetry breaking terms. The resulting effective theory is a bi-scalar tensor theory of gravity. In this theory, the scalar degrees of freedom can be stabilized naturally without the introduction of additional mechanisms other than the appropriate BPS potential. We place observational constraints on the shape of the potential and the global configuration of branes.Comment: 10 pages, 1 figur

A Note on (D(p-2),Dp) Bound State and Noncommutative Yang-Mills Theory

We give a microscopic explanation for the recently observed equivalence among thermodynamics of supergravity solutions for Dp-branes with or without NS B-field and for D(p-2)-branes with vanishing B-field and two delocalized transverse directions by showing that these D-brane configurations are related to one another through T-duality transformations. This result also gives an evidence for the equivalence among the noncommutative and the ordinary Yang-Mills theories corresponding to the decoupling limits of the worldvolume theories of such D-brane configurations.Comment: 13 pages, LaTe

Low Energy Branes, Effective Theory and Cosmology

The low energy regime of cosmological BPS-brane configurations with a bulk scalar field is studied. We construct a systematic method to obtain five-dimensional solutions to the full system of equations governing the geometry and dynamics of the bulk. This is done for an arbitrary bulk scalar field potential and taking into account the presence of matter on the branes. The method, valid in the low energy regime, is a linear expansion of the system about the static vacuum solution. Additionally, we develop a four-dimensional effective theory describing the evolution of the system. At the lowest order in the expansion, the effective theory is a bi-scalar tensor theory of gravity. One of the main features of this theory is that the scalar fields can be stabilized naturally without the introduction of additional mechanisms, allowing satisfactory agreement between the model and current observational constraints. The special case of the Randall-Sundrum model is discussed.Comment: 19 pages, 4 figure

The Effective Energy-Momentum Tensor in Kaluza-Klein Gravity With Large Extra Dimensions and Off-Diagonal Metrics

We consider a version of Kaluza-Klein theory where the cylinder condition is not imposed. The metric is allowed to have explicit dependence on the "extra" coordinate(s). This is the usual scenario in brane-world and space-time-matter theories. We extend the usual discussion by considering five-dimensional metrics with off-diagonal terms. We replace the condition of cylindricity by the requirement that physics in four-dimensional space-time should remain invariant under changes of coordinates in the five-dimensional bulk. This invariance does not eliminate physical effects from the extra dimension but separates them from spurious geometrical ones. We use the appropriate splitting technique to construct the most general induced energy-momentum tensor, compatible with the required invariance. It generalizes all previous results in the literature. In addition, we find two four-vectors, J_{m}^{mu} and J_{e}^{mu}, induced by off-diagonal metrics, that separately satisfy the usual equation of continuity in 4D. These vectors appear as source-terms in equations that closely resemble the ones of electromagnetism. These are Maxwell-like equations for an antisymmetric tensor {F-hat}_{mu nu} that generalizes the usual electromagnetic one. This generalization is not an assumption, but follows naturally from the dimensional reduction. Thus, if {F-hat}_{mu nu} could be identified with the electromagnetic tensor, then the theory would predict the existence of classical magnetic charge and current. The splitting formalism used allows us to construct 4D physical quantities from five-dimensional ones, in a way that is independent on how we choose our space-time coordinates from those of the bulk.Comment: New title, editorial changes made as to match the version to appear in International Journal of Modern Physics

Average R\'enyi Entanglement Entropy in Gaussian Boson Sampling

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian Boson Sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this work, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various R\'enyi-$\alpha$ entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for $\alpha = 1$ (i.e. the von Neumann entropy), and, more generally, for all positive integer $\alpha$, in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the R\'enyi-$\alpha$ variance for integers $\alpha > 1$, and we are able to show that these entropies are weakly typical.Comment: 7+11 pages, 1+2 figure

Open String Tachyon in Supergravity Solution

We study the tachyon condensation of the D-\bar{D}-brane system with a constant tachyon vev in the context of classical solutions of the Type II supergravity. We find that the general solution with the symmetry ISO(1,p)xSO(9-p) (the three-parameter solution) includes the extremal black p-brane solution as an appropriate limit of the solution with fixing one of the three parameters (c_1). Furthermore, we compare the long distance behavior of the solution with the massless modes of the closed strings from the boundary state of the D-\bar{D}-brane system with a constant tachyon vev. We find that we must fix c_1 to zero and the only two parameters are needed to express the tachyon condensation of the D\={D}-brane system. This means that the parameter $c_1$ does not correspond to the tachyon vev of the D\={D}-brane system.Comment: 20 pages, no figures, LaTeX2e, typos corrected, references added and more general result presente