An Exact Operator That Knows Its Location

Abstract

We use conformal symmetry to define an AdS${}_3$ proto-field $\varphi$ as an exact linear combination of Virasoro descendants of a CFT${}_2$ primary operator $\mathcal{O}$. We find that both symmetry considerations and a gravitational Wilson line formalism lead to the same results. The operator $\varphi$ has many desirable properties; in particular it has correlators that agree with gravitational perturbation theory when expanded at large $c$, and that automatically take the correct form in all vacuum AdS${}_3$ geometries, including BTZ black hole backgrounds. In the future it should be possible to use $\varphi$ to probe bulk locality and black hole horizons at a non-perturbative level.

24+33 pages, 2 figures; V2: refs added, terminology updated

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Cited by in corpus (32)

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• Gauge-invariant observables, gravitational dressings, and holography in AdS
• Conformal blocks from Wilson lines with loop corrections
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$
• A Simple Worldsheet Black Hole
• Quantum information geometry of driven CFTs
• Renormalization of gravitational Wilson lines
• Scalar Blocks as Gravitational Wilson Networks
• Superconformal blocks from Wilson lines with loop corrections
• Emergence of spacetime from the algebra of total modular Hamiltonians
• The AdS${}_3$ Propagator and the Fate of Locality
• The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
• Does boundary quantum mechanics imply quantum mechanics in the bulk?
• A Toy Model of the Information Paradox in Empty Space
• Corrections in the relative entropy of black hole microstates
• Modular Hamiltonians and large diffeomorphisms in $Ad{S}_3$
• Four-point conformal blocks with three heavy background operators
• Holographic relations for OPE blocks in excited states
• Inverse problem of correlation functions in holography
• Lectures on Bulk Reconstruction
• Dressing bulk fields in AdS${}_3$
• AdS${}_3$ Reconstruction with General Gravitational Dressings
• Note on Bulk Reconstruction in AdS${}_3$/WCFT${}_2$
• Reconstructing bulk equation of motion using CFT modular Hamiltonians
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$
• On the Stress Tensor Light-ray Operator Algebra
• Dressing bulk spinor fields in AdS${}_3$