dS/CFT and spacetime topology
نویسندگان
چکیده
In the general Euclidean formulation of the AdS/CFT correspondence put forth in [25], one considers Riemannian manifolds of the form M × Y , where M is conformally compactifiable with conformal boundaryat-infinity N. It is then a problem of fundamental interest to determine, for a given compact manifold N with a given conformal structure, the complete Einstein manifolds of negative Ricci curvature having N as conformal boundary. An early result of this type, predating AdS/CFT, was obtained by Graham and Lee [16], who showed that for a conformal structure sufficiently close to the standard one on S, there is a unique Einstein metric with a prescribed curvature close to the standard hyperbolic metric on the n+ 1 ball which induces the conformal boundary N .
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