Holography from Conformal Field Theory

TL;DR

This paper explores the conditions under which a conformal field theory (CFT) admits a local bulk dual in AdS space, establishing that a large-N expansion and a spectral gap imply a local holographic description.

Contribution

It proves that CFTs with a planar expansion and a spectral gap correspond to local bulk theories, confirming the holographic duality under these conditions.

Findings

CFTs with a gap and planar expansion have local bulk duals.

Crossing symmetry constrains the CFT to have a holographic dual.

Explicit solutions support the conjecture.

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.