The Tortoise and the Hare: A Causality Puzzle in AdS/CFT

Abstract

We pose and resolve a holographic puzzle regarding an apparent violation of causality in AdS/CFT. If a point in the bulk of $AdS$ moves at the speed of light, the boundary subregion that encodes it may need to move superluminally to keep up. With $Ad{S}_3$ as our main example, we prove that the finite extent of the encoding regions prevents a paradox. We show that the length of the minimal-size encoding interval gives rise to a tortoise coordinate on $\mathrm{AdS}$ that measures the nonlocality of the encoding. We use this coordinate to explore circular and radial motion in the bulk before passing to the analysis of bulk null geodesics. For these null geodesics, there is always a critical encoding where the possible violation of causality is barely avoided. We show that in any other encoding, the possible violation is subcritical.

28 pages, 14 figures. Matches published version

References in corpus (18)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Theorems on gravitational time delay and related issues
• Averaged Null Energy Condition from Causality
• Proof of the Quantum Null Energy Condition
• Black Holes and Wormholes in 2+1 Dimensions
• Light Rays, Singularities, and All That
• A holographic proof of the averaged null energy condition
• Classics Illustrated: Limits of Spacetimes
• Locality from Quantum Gravity: All or Nothing

Cited by in corpus (5)

• Causal Structures and Nonlocality in Double Holography
• Weak Gravity Conjecture from Conformal Field Theory: A Challenge from Hyperscaling Violating and Kerr-Newman-AdS Black Holes
• Black hole bulk-cone singularities
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Boundary Causality Violating Metrics in Holography