Looking for a bulk point

Abstract

We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.

60 pages, 12 figures

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• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
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• Non-Abelian Binding Energies from the Lightcone Bootstrap
• Conformal Field Theories and Deep Inelastic Scattering
• Looking for (and not finding) a bulk brane
• N=4 Superconformal Bootstrap of the K3 CFT
• On Information Loss in AdS${}_3$/CFT${}_2$
• Pseudo-local Theories: A Functional Class Proposal
• Sub-AdS Scale Locality in AdS${}_3$/CFT${}_2$
• Explicit reconstruction of the entanglement wedge
• The Dual Conformal Box Integral in Minkowski Space
• Into the Bulk: A Covariant Approach
• Semiclassical OPE coefficients from 3D gravity
• Conformal Blocks Beyond the Semi-Classical Limit
• Long-Range Nonlocality in Six-Point String Scattering: simulation of black hole infallers
• A Quantum Correction To Chaos
• Genus Two Modular Bootstrap
• Causal Density Matrices