By Olivier Biquard
Due to the fact its discovery in 1997 by way of Maldacena, AdS/CFT correspondence has turn into one of many top topics of curiosity in string idea, in addition to one of many major assembly issues among theoretical physics and arithmetic. at the actual part, it presents a duality among a thought of quantum gravity and a box concept. The mathematical counterpart is the relation among Einstein metrics and their conformal barriers. The correspondence has been intensively studied, and many development emerged from the disagreement of viewpoints among arithmetic and physics. Written via top specialists and directed at study mathematicians and theoretical physicists in addition to graduate scholars, this quantity provides an outline of this crucial region either in theoretical physics and in arithmetic. It includes survey articles giving a huge evaluate of the topic and of the most questions, in addition to extra really expert articles delivering new perception either at the Riemannian part and at the Lorentzian facet of the idea. A e-book of the eu Mathematical Society. allotted in the Americas by means of the yankee Mathematical Society.
Read or Download IRMA lectures in mathematics and theoretical physics: AdS/CFT correspondence: Einstein metrics and their conformal boundaries. 73rd meeting of theoretical physicists and mathematicians, 2003 PDF
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Additional info for IRMA lectures in mathematics and theoretical physics: AdS/CFT correspondence: Einstein metrics and their conformal boundaries. 73rd meeting of theoretical physicists and mathematicians, 2003
Carlip, J. Ratcliffe, S. Surya and S. Tschantz, Peaks in the HartleHawking wave function from sums over topologies, Classical Quantum Gravity 21 (2004), 729–741.  M. Anderson, P. Chru´sciel and E. Delay, Non-trivial static, geodesically complete vacuum space-times with a negative cosmological constant, J. High Energy Phys. 10 (2002), 063.  L. Andersson and G. Galloway, dS/CFT and spacetime topology, Adv. Theor. Math. Phys. 6 (2003), 307–327.  V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Comm.
3. Let (S, g) be an (n+1) dimensional globally hyperbolic space-time, with compact Cauchy surface , which is C 3 conformally compact to the past, so that 25 Geometric aspects of the AdS/CFT correspondence past conformal infinity ( decay conditions −, γ ) is C 3 . 15) for T time-like. Let γ be a representative for [γ ] with constant scalar curvature Rγ . 16) where ρ is the geodesic defining function associated to ( − , γ ). In particular, any time-like geodesic in S is future incomplete, and no Cauchy surface ρ exists, even partially, for ρ 2 > 4n(n − 1)/|Rγ |, so that + = ∅.
Since the two analytic continuation procedures are equivalent and finite, (I) manifestly so, while in (II), the singularity can be regulated by an i prescription inherent in the analytic continuation procedure, and the contribution from the past and future singularity can be shown to cancel. Its not entirely clear how much information behind the horizon can really be inferred from this procedure: the fact that we can obtain the same correlation function by integrating in the region outside the horizon seems to suggest that no real information behind the horizon can really be contained in these correlations functions.