We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The ’t Hooft limit of 3+1 N = 4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various AntideSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five or four non-compact dimensions. 1

We study a quotient Conformal Field Theory, which describes a 3 + 1 dimensional cosmological spacetime. Part of this spacetime is the Nappi-Witten (NW) universe, which starts at a “big bang ” singularity, expands and then contracts to a “big crunch ” singularity at a finite time. The gauged WZW model contains a number of copies of the NW spacetime, with each copy connected to the preceeding one and to the next one at the respective big bang/big crunch singularities. The sequence of NW spacetimes is further connected at the singularities to a series of non-compact static regions with closed timelike curves. These regions contain boundaries, on which the observables of the theory live. This suggests a holographic interpretation of the physics. 4/02

We analyze the structure of supersymmetric Gödel-like cosmological solutions of string theory. Just as the original four-dimensional Gödel universe, these solutions represent rotating, topologically trivial cosmologies with a homogeneous metric and closed timelike curves. First we focus on “phenomenological ” aspects of holography, and identify the preferred holographic screens associated with inertial comoving observers in Gödel universes. We find that holography can serve as a chronology protection agency: The closed timelike curves are either hidden behind the holographic screen, or broken by it into causal pieces. In fact, holography in Gödel universes has many features in common with de Sitter space, suggesting that Gödel universes could represent a supersymmetric laboratory for addressing the conceptual puzzles of de Sitter holography. Then we initiate the investigation of “microscopic ” aspects of holography of Gödel universes in string theory. We show that Gödel universes are T-dual to pp-waves, and use this fact to generate new Gödel-like solutions of string and M-theory by T-dualizing known supersymmetric pp-wave solutions. December

hep-th/9910174

ABSTRACT: A family of exact conformal field theories is constructed which describe charged black strings in three dimensions. Unlike previous charged black hole or extended black hole solutions in string theory, the low energy spacetime metric has a regular inner horizon (in addition to the event horizon) and a timelike singularity. As the charge to mass ratio approaches unity, the event horizon remains but the singularity disappears

We review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non–experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kähler geometry and geometric mechanics how they could perform their results in order to be accepted by the community of ”orthodox ” physicists. Although the bulk of former models of Finsler–Lagrange spaces where elaborated on tangent bundles, the surprising result advocated in our works is that such locally anisotropic structures can be modelled equivalently on Riemann–Cartan spaces, even as exact solutions in Einstein and/or string gravity, if nonholonomic distributions and moving frames of references are introduced into consideration.

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Abstract: This course provides a self contained introduction to the general theory of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined to a worldsheet of the corresponding dimension (respectively one, two, and three) in a thin limit approximation. The first part of the course is concerned with purely kinematic aspects: it is shown how, to second differential order, the geometry (and in particular the inner and outer curvature) of a brane worldsheet of arbitrary dimension is describable in terms of the first, second, and third fundamental tensor; the extension to a foliation by a congruence of such worldsheets is also briefly discussed. In the next part, it is shown how – to lowest order in the thin limit – the evolution of such a brane worldsheet will always be governed by a simple tensorial equation of motion whose left hand side is the contraction of the relevant surface stress tensor T µν with the (geometrically defined) second fundamental tensor Kµν ρ, while the right hand side will simply vanish in the case of free motion and will otherwise be just the

We consider solutions to the linear wave equation ✷gφ = 0 on a nonextremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In particular, no symmetry is assumed on initial data, and the support of the solutions may contain the sphere of bifurcation of the black/white hole horizons and the cosmological horizons.) We prove that in the region bounded by a set of black/white hole horizons and cosmological horizons, solutions φ converge pointwise to a constant faster than any given polynomial rate, where the decay is measured with respect to natural future-directed advanced and retarded time coordinates. We also give such uniform decay bounds for the energy associated to the Killing field as well as for the energy measured by local observers crossing the event horizon. The results in particular include decay rates along the horizons themselves. Finally, we discuss the relation of these results to previous heuristic analysis of Price and Brady et al. Contents 1

In this article, we review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non–experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kähler geometry and geometric mechanics how they could perform their results in order to be accepted by the community of ”orthodox ” physicists. Although the bulk of former models of Finsler–Lagrange spaces where elaborated on tangent bundles, the surprising result advocated in our works is that such locally anisotropic structures can be modelled equivalently on Riemann–Cartan spaces, even as exact solutions in Einstein and/or string gravity, if nonholonomic distributions and moving frames of references are introduced into consideration.