A Holographic Dual of the Quantum Inequalities

Abstract

In this note, we establish the 2-D Quantum Inequalities - first proved by Flanagan - for all CFTs with a causal holographic dual. Following the treatment of Kelly \& Wall, we establish that the Boundary Causality Condition in an asymptotic AdS spacetime implies the Quantum Inequalities on the boundary. Our results extend easily to curved spacetime and are stable under deformations of the CFT by relevant operators. We discuss higher dimensional generalizations and possible connections to recent bounds on $a/c$ in 4-D CFTs.

arXiv comment5 pages, 1 figure

References in corpus (14)

• Averaged Energy Conditions and Quantum Inequalities
• Theorems on gravitational time delay and related issues
• Proof of the Quantum Null Energy Condition
• Restrictions on Negative Energy Density in Flat Spacetime
• Quantum inequalities in two dimensional Minkowski spacetime
• A Proof of the Conformal Collider Bounds
• Bounds on negative energy densities in flat spacetime
• Quantum Energy Inequalities in two-dimensional conformal field theory
• The Quantum Interest Conjecture
• Holographic Proof of the Quantum Null Energy Condition
• Entanglement entropy and negative energy in two dimensions
• A holographic proof of the averaged null energy condition
• Quantum inequalities in two dimensional curved spacetimes
• The Gravity Dual of Boundary Causality

Cited by in corpus (2)

• The Smeared Null Energy Condition
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