Restricted Quantum Focusing

TL;DR

This paper introduces a weaker form of the quantum focusing conjecture, demonstrating its sufficiency for key quantum gravity implications and proving it in certain holographic dual theories.

Contribution

It proposes a restricted quantum focusing conjecture and proves it for brane-world semiclassical gravity theories holographically dual to Einstein gravity.

Findings

Restricted quantum focusing suffices for known quantum gravity implications.

Proof of the conjecture in holographic dual theories.

Supports the conjecture's relevance in quantum gravity frameworks.

Abstract

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.