Restricted Quantum Focusing

Quantum Focusing is a powerful conjecture, which plays a key role in the current proofs of many well-known quantum gravity theorems, including various consistency conditions, and causality constraints in AdS/CFT. I conjecture a (weaker) restricted quantum focusing, which I argue is sufficient to derive all known essential implications of quantum focusing. Subject to a technical assumption, I prove this conjecture on brane-world semiclassical gravity theories which are holographically dual to Einstein gravity in a higher dimensional anti-de Sitter spacetime.