THE EINSTEIN EQUATION IN A THEORY OF STRINGS

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein-like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for space–time gravity, even in the absence of other matter fields.

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Gravity in a warped 6D world with an extra 2D sphere

International Journal of Modern Physics D ◽

10.1142/s0218271819500299 ◽

2019 ◽

Vol 28 (02) ◽

pp. 1950029

Author(s):

Akira Kokado ◽

Takesi Saito

Keyword(s):

Differential Equation ◽

Einstein Equation ◽

Infinite Series ◽

Energy Momentum Tensor ◽

Momentum Tensor ◽

Special Choice ◽

Higher Dimensional ◽

General Energy ◽

Yukawa Potentials ◽

Matter Fields

Corrections to Newton’s inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here, we give a model of a warped 6D world with an extra 2D sphere. We take a general energy–momentum tensor, which does not depend on a special choice of bulk matter fields. The 6D Einstein equation reduces to the spheroidal differential equation, which can be easily solved. The gravitational potential in our 4D universe is calculated to be composed of infinite series of massive Yukawa potentials coming from the KK mode, together with Newton’s inverse law. The series of Yukawa type potentials converges well to behave as [Formula: see text] near [Formula: see text].

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Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

EPJ Web of Conferences ◽

10.1051/epjconf/201817511007 ◽

2018 ◽

Vol 175 ◽

pp. 11007 ◽

Cited By ~ 1

Author(s):

Christof Gattringer ◽

Daniel Göschl ◽

Carlotta Marchis

Keyword(s):

Degrees Of Freedom ◽

Chemical Potential ◽

Space Time ◽

Field Theories ◽

Gauge Fields ◽

Chiral Model ◽

Staggered Fermions ◽

Lattice Field ◽

Principal Chiral Model ◽

Matter Fields

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

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COSMIC DEFECT COSMOLOGY

International Journal of Modern Physics A ◽

10.1142/s0217751x0904511x ◽

2009 ◽

Vol 24 (08n09) ◽

pp. 1620-1624

Author(s):

A. TARTAGLIA

Keyword(s):

Phase Space ◽

Cold Dark Matter ◽

Displacement Vector ◽

Empty Space ◽

Space Time ◽

Point Particle ◽

Accelerated Expansion ◽

Displacement Vector Field ◽

Type Ia ◽

Ia Supernovae

The accelerated expansion of the universe is interpreted as an effect of a defect in space-time treated as a four-dimensional continuum endowed with physical properties. The analogy is with texture defects in material continua, like dislocations and disclinations, described in terms of a singular displacement vector field. A Lagrangian for empty space-time is proposed exploiting one further analogy between the phase space of a Robertson-Walker universe and the phase space of a point particle moving across an homogeneous isotropic medium. The model, named Cosmic Defect theory, produces, as a byproduct, also inflation near the initial singularity. The theory has been applied to fit the luminosity data of 192 type Ia supernovae. The results are satisfying and comparable with the ones obtained by means of the Λ Cold Dark Matter standard model.

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Internal wave evolution in a space–time varying field

Journal of Fluid Mechanics ◽

10.1017/s0022112000001841 ◽

2000 ◽

Vol 424 ◽

pp. 279-301 ◽

Cited By ~ 12

Author(s):

D. A. HORN ◽

L. G. REDEKOPP ◽

J. IMBERGER ◽

G. N. IVEY

Keyword(s):

Kdv Equation ◽

Background Field ◽

Variable Coefficients ◽

Space Time ◽

Topographic Effects ◽

Time Varying ◽

Weakly Nonlinear ◽

Natural Systems ◽

Lower Depth ◽

Spatially Varying

An extended Korteweg–de Vries (KdV) equation is derived that describes the evolution and propagation of long interfacial gravity waves in the presence of a strong, space–time varying background. Provision is made in the derivation for a spatially varying lower depth so that some topographic effects can also be included. The extended KdV model is applied to some simple scenarios in basins of constant and varying depths, using approximate expressions for the variable coefficients derived for the case when the background field is composed of a moderate-amplitude ultra-long wave. The model shows that energy can be transferred either to or from the evolving wave packet depending on the relative phases of the evolving waves and the background variation. Comparison of the model with laboratory experiments confirms its applicability and usefulness in examining the evolution of weakly nonlinear waves in natural systems where the background state is rarely uniform or steady.

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Nonsingular cosmological model with background field in flat space-time theory of gravitation

Astrophysics and Space Science ◽

10.1007/bf00627088 ◽

1994 ◽

Vol 222 (1-2) ◽

pp. 127-145 ◽

Cited By ~ 2

Author(s):

Walter Petry

Keyword(s):

Cosmological Model ◽

Flat Space ◽

Background Field ◽

Space Time ◽

Theory Of Gravitation ◽

Nonsingular Cosmological Model ◽

Time Theory

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

Communications in Physics ◽

10.15625/0868-3166/28/3/12583 ◽

2018 ◽

Vol 28 (3) ◽

pp. 277

Author(s):

Phan Hong Lien

Keyword(s):

Einstein Equation ◽

Dimensional Space ◽

Equations Of Motion ◽

Space Time ◽

Cosmological Evolution ◽

System Of Equations ◽

Dimensional Space Time ◽

Six Dimensions ◽

Bulk Space

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.

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