Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT

2011/04/13 by Daniel Harlow, Douglas Stanford, Harlow, Daniel +1 · 15 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.48550/arxiv.1104.2621

21 pages plus appendices, 6 figures, typos corrected

openalex publication_date 2011/04/13 · arxiv created 2011/04/21 · arxiv updated 2011/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Dual AdS/CFT correlators can be computed in two ways: differentiate the bulk partition function with respect to boundary conditions, or extrapolate bulk correlation functions to the boundary. These dictionaries were conjectured to be equivalent by Banks, Douglas, Horowitz, and Martinec. We revisit this question at the level of bulk path integrals, showing that agreement in the presence of interactions requires careful treatment of the renormalization of bulk composite operators. By contrast, we emphasize that proposed dS/CFT analogues of the two dictionaries are inequivalent. Next, we show quite generally that the wave function for Euclidean AdS analytically continues to the dS wave function with Euclidean initial conditions. Most of our arguments consider interacting fields on a fixed background, but in a final section we discuss the inclusion of bulk dynamical gravity.

Citations

• Quantum Gravity In De Sitter Space
• S-Matrices from AdS Spacetime
• The Holographic Bound in Anti-de Sitter Space
• The dS/CFT correspondence
• Introduction to Gauge/Gravity Duality

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• Toward a Consistent Definition of Holographic Entanglement Entropy in de Sitter Space
• Toward Holography on Biregular Trees
• Celestial Holography meets dS/CFT
• Decoupling of High Dimension Operators from the Low Energy Sector in Holographic Models
• The Three Faces of a Fixed Point
• BICEP2 and the Central Charge of Holographic Inflation
• The AdS/CFT partition function, AdS as a lift of a CFT, and holographic RG flow from conformal deformations
• The inflationary wavefunction from analyticity and factorization
• Constraints on Symmetries from Holography
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• Simple Bulk Reconstruction in AdS/CFT Correspondence
• Bulk-boundary dictionary for a non local bulk field
• Dynamics of Heavy Operators in AdS/CFT
• AdS/CFT Correspondence Beyond its Supergravity Approximation
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