scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

INDUCED PARITY VIOLATION ANOMALY FOR THE PROCA FIELD IN A THREE-DIMENSIONAL SPACE–TIME

1999 ◽  
Vol 14 (02) ◽  
pp. 271-280
Author(s):  
E. R. BEZERRA DE MELLO ◽  
V. M. MOSTEPANENKO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Nonrelativistic Limit ◽  
Space Time ◽  
Simons Theory ◽  
Proca Field ◽  
Dimensional Space Time ◽  
Chern Simons ◽  
Three Dimensional Space ◽  
Chern Simons Theory

In this paper we develop diagrammatic computations of spontaneous parity-violating anomalies for a complex massive vector field (Proca field) induced by its interaction with an electromagnetic field in a three-dimensional space–time. We also calculate the effective potential energy between two charged particles in Maxwell–Chern–Simons theory in a nonrelativistic limit.

scholarly journals THE STRUCTURE OF ADS BLACK HOLES AND CHERN–SIMONS THEORY IN 2 + 1 DIMENSIONS

1999 ◽  
Vol 14 (04) ◽  
pp. 505-520 ◽  
Author(s):  
SHARMANTHIE FERNANDO ◽  
FREYDOON MANSOURI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gauge Theory ◽  
Excited States ◽  
Simons Theory ◽  
De Sitter ◽  
Sitter Group ◽  
Ads Black Holes ◽  
Chern Simons ◽  
Chern Simons Theory

We study anti-de Sitter black holes in 2 + 1 dimensions in terms of Chern–Simons gauge theory of the anti-de Sitter group coupled to a source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how all the relevant features of the black hole are accounted for. The requirement that the source be a unitary representation leads to a discrete tower of excited states which provide a microscopic model for the black hole.

EXACT SOLUTIONS FOR SELF-DUAL SU(2) GAUGE THEORY WITH AXIAL SYMMETRY

2001 ◽  
Vol 16 (11) ◽  
pp. 685-692 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
C. BANDAC
Keyword(s):  
Gauge Theory ◽  
Axial Symmetry ◽  
Dimensional Space ◽  
Space Time ◽  
Field Equations ◽  
Metric Tensor ◽  
Gauge Invariant ◽  
Local Gauge ◽  
Dimensional Space Time ◽  
Strength Tensor

A model of SU(2) gauge theory is constructed in terms of local gauge-invariant variables defined over a four-dimensional space–time endowed with axial symmetry. A metric tensor gμν is defined starting with the components [Formula: see text] of the strength tensor and its dual [Formula: see text]. The components gμν are interpreted as new local gauge-invariant variables. Imposing the condition that the new metric coincides with the initial metric we obtain the field equations for the considered ansatz. We obtain the same field equations using the condition of self-duality. It is concluded that the self-dual variables are compatible with the axial symmetry of the space–time. A family of analytical solutions of the gauge field equations is also obtained. The solutions have the confining properties. All the calculations are performed using the GRTensorII computer algebra package, running on the MapleV platform.

scholarly journals HIGHER DIMENSIONAL DUST COSMOLOGICAL IMPLICATIONS OF A DECAY LAW FOR THE Λ TERM: EXPRESSIONS FOR SOME OBSERVABLE QUANTITIES

2006 ◽  
Vol 15 (01) ◽  
pp. 95-105 ◽  
Author(s):  
G. S. KHADEKAR ◽  
ANIRUDH PRADHAN ◽  
M. R. MOLAEI
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Nucl Phys ◽  
De Sitter ◽  
Angular Diameter Distance ◽  
Proper Distance ◽  
Higher Dimensional ◽  
Significant Difference ◽  
Dimensional Space Time ◽  
Sitter Model

We have considered the multidimensional cosmological implications of a decay law for the Λ term that is proportional to [Formula: see text], where β is a constant and a is the scale factor of RW-space–time. We discuss the cosmological consequences of a model for the vanishing pressure for the case k = 0. It has been observed that such models are compatible with the result of recent observations and the cosmological term Λ gradually reduces as the universe expands. In this model, Λ varies as the inverse square of time, which matches its natural units. The proper distance, the luminosity distance-redshift, the angular diameter distance-redshift, and look back time-redshift for the model are presented in the framework of higher dimensional space–time. The model of the Freese et al. (Nucl. Phys. B287, 797 (1987)) for n = 2 is retrieved for the particular choice of A0and also the Einstein–de Sitter model is obtained for [Formula: see text]. This work has thus generalized to higher dimensions the well-known result in four-dimensional space–time. It is found that there may be a significant difference, in principle at least, to the analogous situation in four-dimensional space–time.

scholarly journals The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
J. A. Helayël-Neto ◽  
Alireza Sepehri ◽  
Tooraj Ghaffary
Keyword(s):  
Modified Gravity ◽  
Dimensional Space ◽  
Main Idea ◽  
Big Bang ◽  
Space Time ◽  
Dimensional Manifold ◽  
3 Dimensional ◽  
Dimensional Space Time ◽  
The Big Bang ◽  
Chern Simons

It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.

scholarly journals THE WARPING OF EXTRA SPACES ACCELERATES THE EXPANSION OF THE UNIVERSE

2010 ◽  
Vol 19 (14) ◽  
pp. 2281-2287 ◽  
Author(s):  
ISHWAREE P. NEUPANE
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
De Sitter ◽  
Four Dimensions ◽  
Accelerating Expansion ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Expansion Of The Universe ◽  
Theories Of Gravity ◽  
The Universe

Generic cosmological models derived from higher-dimensional theories with warped extra-dimensions have a nonzero cosmological constant-like term induced on the 3 + 1 space–time, or a physical three-brane. In the scenario where this 3 + 1 space–time is an inflating de Sitter "bran" embedded in a higher-dimensional space–time, described by warped geometry, the four-dimensional cosmological term is determined in terms of two length scales: one is a scale associated with the size of extra-dimension(s) and the other is a scale associated with the warping of extra-space(s). The existence of this term in four dimensions provides a tantalizing possibility of explaining the observed accelerating expansion of the universe from fundamental theories of gravity, e.g. string theory.

Geometrical particles and dualities related to curves in null de Sitter 3-sphere

2021 ◽  
pp. 2150152
Author(s):  
Xue Song ◽  
Donghe Pei
Keyword(s):  
Duality Theory ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Dual Relationships ◽  
De Sitter ◽  
Contact Manifolds ◽  
Dimensional Space Time ◽  
Three Dimensional Space

In this paper, we confine the trajectory of geometrical particles to the de Sitter three-dimensional space–time, we model geometrical particles as spacelike tachyons. Using the Legendrian duality theory of pseudo-spheres and contact manifolds theory we establish the dual relationships between spacelike moving trajectory of geometrical particles and future nullcone hypersurfaces.

CHRONOMETRIC INVARIANCE AND STRING THEORY

2008 ◽  
Vol 23 (11) ◽  
pp. 797-813 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Physical Space ◽  
Space Time ◽  
Kerr Metric ◽  
De Sitter ◽  
Superstring Theory ◽  
Dimensional Space Time ◽  
Raychaudhuri Equations ◽  
Three Space

The Einstein–Hilbert Lagrangian R is expressed in terms of the chronometrically invariant quantities introduced by Zel'manov for an arbitrary four-dimensional metric gij. The chronometrically invariant three-space is the physical space γαβ = -gαβ+e2ϕ γαγβ, where e 2ϕ = g00 and γα = g0α/g00, and whose determinant is h. The momentum canonically conjugate to γαβ is [Formula: see text], where [Formula: see text] and ∂t≡ e -ϕ∂0 is the chronometrically invariant derivative with respect to time. The Wheeler–DeWitt equation for the wave function Ψ is derived. For a stationary space-time, such as the Kerr metric, παβ vanishes, implying that there is then no dynamics. The most symmetric, chronometrically-invariant space, obtained after setting ϕ = γα = 0, is [Formula: see text], where δαβ is constant and has curvature k. From the Friedmann and Raychaudhuri equations, we find that λ is constant only if k=1 and the source is a perfect fluid of energy-density ρ and pressure p=(γ-1)ρ, with adiabatic index γ=2/3, which is the value for a random ensemble of strings, thus yielding a three-dimensional de Sitter space embedded in four-dimensional space-time. Furthermore, Ψ is only invariant under the time-reversal operator [Formula: see text] if γ=2/(2n-1), where n is a positive integer, the first two values n=1,2 defining the high-temperature and low-temperature limits ρ ~ T±2, respectively, of the heterotic superstring theory, which are thus dual to one another in the sense T↔1/2π2α′T.

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