Pdf oscillating shells in antide sitter space researchgate. Furthermore, this result is required by a general covariance argument. In this description, quantum phenomena such as the spontaneous breaking of the center. Conformal invariance, nextended supersymmetry and massless. A conjugation on the quantum ads algebra is deduced from the corresponding conjugation on the quantum ads group. Analytical expressions are found for the field modes and feynman green function. Socolovsky, schwarzschild black hole in antide sitter space arxiv. Antide sitter timelike geodesics are ellipses and are obtained by intersecting the hyperboloid with. Here we elaborate on this idea and propose a precise correspondence between conformal field theory. Abstract recently, it has been proposed by maldacena that large n limits of certain conformal field theories in d dimensions can be described. Treating the kantowskisachs metric in the same way we obtain. Particular care is taken over the distinction between antidesitter and its covering space. Coley physics scripta 92, 093003 2017 mostly but not exclusively in cosmology and.
In mathematics and physics, ndimensional antide sitter space ads n is a maximally symmetric lorentzian manifold with constant negative scalar curvature. Thermodynamics of black holes in antide sitter space. A 2adic arithmetic geometryversion of ads spacetime is identified with the bruhattits tree for the projective general linear group pgl 2. Furthermore, we investigate the type number of the pseudo. Recently, antide sitter space has appeared in a surprising new context. The einstein equations with a negative cosmological constant admit black hole solutions which are asymptotic to antide sitter space. Let us begin with a survey of the ads space and the schwarzschildads black hole.
In mathematics and physics, ndimensional antide sitter space is a maximally symmetric lorentzian manifold with constant negative scalar curvature. We start by proposing a relation between supersymmetric black holes in four and ve. The ads space is a solution of the einstein equation with a negative cosmological constant r ij g ij. Maldacena 4 has conjectured that the large nlimit of certain super conformal theories are equivalent to a string theory on a background containing the direct product of antide sitter space in ve dimensions times a compact manifold. Asymptotically antide sitter spaces play a central role in the realization of the holographic principle by adscft correspondence in p padic geometry. This is a pedagogic account of some of the global properties of antidesitter spacetime with a view to their application to the adscft correspondence. Jan 07, 20 the video clearly shows space and particles reacting to audio waves. The action obtained possesses both gauge nextended worldline supersymmetry and local on invarince. Introduction to the adscft correspondence by horatiu nastase september 2015. The action obtained possesses both gauge nextended. Antidesitter grwiki antidesitter spacetime and its uses by gary w. Oscillating shells in antide sitter space javier mas and alexandre serantes. A differential calculus on the quantum ads space is introduced. Gibbons 199809 an introduction to gauge gravity duality and its application in condensed matter by andrew g.
Which the quantum world behaves in a similar manner, particles dancing on waves. In this paper, we prove the existence of maximal slices in antide sitter spaces ads spaces with small boundary data at spatial infinity. Lorentzian analog of euclidean space, and antide sitter space is the lorenzian analog of hyperbolic space. There is an isometric copy h4 q of hyperbolic space with x 0 sitter space has appeared in a surprising new context. Silverstein proposed this basic idea with three coauthors back in 2004, but new theoretical tools have enabled her, dong and torroba to study the dsds hologram in greater detail and show.
Written version of lectures given at 2nd samos meeting held at at pythagoreon, samos, greece, 31 august 4 september 1998 and published as anti. Maximal slices in antide sitter spaces li, zhenyang and shi, yuguang, tohoku mathematical journal, 2008. Green contemporary physics 54, 33 20 open problems in mathematical physics by alan a. Black holes in antide sitter spacetime semantic scholar. The video clearly shows space and particles reacting to audio waves.
We argue that this difference between the kinetic and the antide sitter spaceconformal field theories is related to the secondorder hydrodynamic coefficient. The antide sitter ads space can be thought to have a potential wall as one approaches the asymptotic in nity. The correspondence between supergravity and string theory on ads space and boundary conformal field theory relates the thermodynamics of superyangmills theory in four dimensions to the thermodynamics of schwarzschild black holes in antide sitter space. Finally, some useful information about the geometric properties of antide sitter spaces and the kerrantide sitter solution is collected in the appendices. As is well known, the theory of minimal surfacessubmanifolds has a long history originating from the papers of lagrange in 1760 and the famous plateau problem. Starting with a manifestly conformal od, 2 invariant mechanics model in d space and two time dimensions, we derive the action for a massless spinning particle in ddimensional antide sitter space. Rather, there is a contribution which scales like r 2, leading to an attractive force, in addition to the gravitational attraction. So, then the desitter space has negative curvature, whereas it is positive for the anti desitter space.
If the above is correct, it implies that the desitter space is akin to the hyperbolic space in terms of the distance measure, whereas anti desitter space is more like the elliptic space. Like black holes in asymptotically flat space, these solutions have thermodynamic properties including a characteristic temperature and an intrinsic entropy equal to one quarter of the area of the event horizon in planck units. We have introduced mainly two types of the metrics for ads 5. Second, our tiny presentday cosmological constant currently accounts for about 68% of the energy density of the universe, and this fraction is growing as the universe continues to expand. Quantum scalar field theory on antide sitter space core. In mathematics and physics, ndimensional antide sitter space adsn is a maximally.
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