Holography from conformal field theory
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 largeN 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 largeN 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 largeN expansion, the fourpoint 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 explicit solutions.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2009
 DOI:
 10.1088/11266708/2009/10/079
 arXiv:
 arXiv:0907.0151
 Bibcode:
 2009JHEP...10..079H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 49 pages. Minor corrections. Figure and references added