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 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 explicit solutions. 5 We thank M. Douglas and S. Giddings for discussions of this possibility. 6 We thank S. Dubovsky and D. Gross for this observation. 7 We thank E. Silverstein for raising this point.

Bulk locality and quantum error correction in AdS/CFT

“…We then use this assumption to perform the Bogoliubov transformation that relates the global and the Rindler reconstructions. This assumption is quite plausible, and essentially follows from the assumed large-N structure of the CFT [39], but it would still be nice if we could explicitly demonstrate the structure of the quantum error correcting code in the CFT. In particular, in section 4.2 we had to use bulk causality to argue that the necessary and sufficient condition (3.28) for operator algebra quantum error correction held, and we were not able to check it explicitly for all possible CFT operators on A.…”

On non-supersymmetric conformal manifolds: field theory and holography

“…(2.7) simplifies to 19) and integrated conformal blocks in eq. (2.14), hence contributions as in figure 2a, would not contribute to (2.16).…”

“…trace operators with spin greater than two have a parametrically large dimension [19]. More precisely, in the large-N limit the CFT reduces to a subset of operators having small dimension (i.e., a dimension ∆ that does not scale with N ), and whose connected n-point functions are suppressed by powers of 1/N .…”

Comments on Rényi entropy in AdS3/CFT2

“…This restricts the OPE coefficients of the theory to scale, at most, exponentially in c. Second, the theory has a gap, in the sense that the density of states of dimension ∆ O(c) grows polynomially with c, at most. 3 Duals to Einstein gravity with a finite number of light fields have an O(c 0 ) density of states below the gap, but these are a mere corner of the general space of holographic CFTs [25,26].…”