By Olivier Biquard
Considering that its discovery in 1997 by way of Maldacena, AdS/CFT correspondence has turn into one of many best matters of curiosity in string conception, in addition to one of many major assembly issues among theoretical physics and arithmetic. at the actual facet, it offers a duality among a concept of quantum gravity and a box idea. The mathematical counterpart is the relation among Einstein metrics and their conformal obstacles. The correspondence has been intensively studied, and many growth emerged from the disagreement of viewpoints among arithmetic and physics. Written by means of prime specialists and directed at learn mathematicians and theoretical physicists in addition to graduate scholars, this quantity provides an summary of this crucial region either in theoretical physics and in arithmetic. It comprises survey articles giving a vast evaluation of the topic and of the most questions, in addition to extra really expert articles offering new perception either at the Riemannian aspect and at the Lorentzian aspect of the speculation. A book of the ecu Mathematical Society. disbursed in the Americas by way of the yankee Mathematical Society.
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Extra info for AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries
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Starting from Lorentzian configurations, one can build configurations with multiple boundary components by taking a 2-dimensional slice of global AdS3 , cutting and gluing it along geodesics and then letting it evolve in time . Such constructions lead, in agreement with the topological censorship theorem, to space-times with the same number h of boundaries and horizons, and with any number g of handles behind the horizons. In the special case where there are only two boundaries (h = 2, g = 0), the space-time describes the eternal BTZ black hole.
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