Tests of restricted Quantum Focusing and a new CFT bound

Abstract

The restricted quantum focusing conjecture (rQFC) plays a central role in an axiomatic formulation of semiclassical gravity. Since much hinges on its validity, it is imperative to subject the rQFC to rigorous tests in novel settings. Here we do so in two independent directions. First, we prove rQFC in a class of spacetime dimension $d=2$ toy models, JT gravity coupled to a QFT. We also construct explicit counter-examples to the original and stronger Quantum Focusing Conjecture in a regime where matter quantum effects are comparable to the total dilaton value. Second, for $d>2$, we derive from the rQFC a constraint stronger than the Quantum Null Energy Condition (QNEC). In a broad class of states, this bound forbids the QNEC from saturating faster than $O(\mathcal{A})$ as the transverse area $\mathcal{A}$ of a certain null deformation shrinks to zero. We speculate about a universal strengthened QNEC holding across all QFT states.

57 pages, 12 figures. Version 1 of this paper emphasized a very weak condition required for the rQFC to hold in d>2. In Version 2, we emphasize a much stronger implication of the rQFC, a strengthened form of the QNEC, and present the weak condition only in an appendix. v3: Published version with minor changes