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NSF-KITP-09-110 Holography from Conformal Field Theory

By Idse Heemskerk, Joao Penedones, Joseph Polchinski and James Sully

Abstract

The locality of bulk physics at distances below the AdS length scale is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large compared to the Planck length and the string length. In the CFT this implies a large-N expansion and a gap in the spectum of anomalous dimensions. We conjecture that the implication also runs in the other direction, so that any CFT with a large-N expansion and a large gap has a local bulk dual. For an abstract CFT we formulate the consistency conditions, most notably crossing symmetry, and show that the conjecture is true in a broad range of CFT’s, to first nontrivial order in 1/N 2: in any CFT with a gap and a large-N expansion, the four-point correlator is generated via the AdS/CFT dictionary from a local bulk interaction. We establish this result by a counting argument on each side, and also investigate various properties of some AdS/CFT duality maps a higher dimensional bulk into a lower dimensional boundary[1, 2, 3]. This means that excitations that are coincident in the boundary CFT may be far apart i

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