A Holographic Dual of the Quantum Inequalities

Understand

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.