Holography from Conformal Field Theory
Abstract
The locality of bulk physics at distances below the AdS length 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 planar 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: any CFT with a gap and a planar expansion 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 explicit solutions.
Cite
@article{arxiv.0907.0151,
title = {Holography from Conformal Field Theory},
author = {Idse Heemskerk and Joao Penedones and Joseph Polchinski and James Sully},
journal= {arXiv preprint arXiv:0907.0151},
year = {2009}
}
Comments
49 pages. Minor corrections. Figure and references added