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.

49 pages. Minor corrections. Figure and references added

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• The Goldstone Equivalence Theorem and AdS/CFT
• Causal Density Matrices
• Bulk Connectedness and Boundary Entanglement
• Constraints on beta functions in field theories
• Response of interferometers to the vacuum of quantum gravity
• Emergent Dark Gravity from (Non)Holographic Screens
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Information recovery from pure state geometries in 3D
• On the Virasoro fusion kernel at $c=25$
• Recursive construction of the operator product expansion in curved space
• Operator product expansions and recoil
• Linear gravity from conformal symmetry
• A Holographic Constraint on Scale Separation
• Correlation functions at the bulk point singularity from the gravitational eikonal S-matrix
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• AdS/CFT for Accelerator Physics or Building the Tower of Babel
• Towards holography for quantum mechanics
• Holographic phenomenology via overlapping degrees of freedom
• QCD, with Strings Attached
• Interplay of Reggeon and photon in pA collisions
• A symmetry principle for emergent spacetime
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories
• Flat-space Quantum Gravity in AdS/CFT
• A proof of Generalized Connected Wedge Theorem
• Flat limit of massless scalar scattering in ${\mathrm{AdS}}_2$
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Conformal bootstrap in momentum space at finite volume
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• Undecidability in Spacetime Geometry via the AdS/CFT Correspondence
• Moments and saddles of heavy CFT correlators
• Constructing CFTs from AdS flows
• Non-local Geometry inside Lifshitz Horizon
• Composite AdS geodesics for CFT correlators and timelike entanglement entropy
• Tenfold Way for Holography : AdS/CFT and Beyond
• Higher-spin localized shocks
• Universal sectors in superconformal defects
• Searching for emergent spacetime in spin glasses
• Searching for strongly coupled AdS matter with multi-trace deformations
• Three-point current correlation functions as probes of Effective Conformal Theories
• Boundary conformal field theory, holography and bulk locality
• A Reverse Black Hole Information Problem