The Quantum Focusing Conjecture Has Not Been Violated

TL;DR

The paper addresses a apparent pointwise violation of the Quantum Focusing Conjecture (QFC) in $d\ge5$ theories with Gauss–Bonnet coupling by Fu, Koeller, and Marolf, and shows that a correct effective-field-theory treatment—where geometric terms are promoted to smeared surface operator expectation values over regions at the cutoff scale—removes the violation. By analyzing the smeared quantum expansion $\langle\Theta\rangle$ and the contributions from $S_{\rm grav}$ and $S_{\rm out}$, the authors demonstrate that the potentially dangerous local terms are either subleading or canceled when smearing is properly implemented, while nonlocal terms remain negative by strong subadditivity. They also discuss how this smearing perspective parallels issues in Entanglement Wedge Nesting (EWN) in holography and may reflect a deeper connection between bulk geometry and boundary subregion duality. The work reinforces the robustness of the QFC within EFT and highlights the essential role of operator smearing in semiclassical gravity and holographic contexts.

Abstract

Recent work of Fu, Koeller, and Marolf shows that in $d\geq 5$ dimensions a nonzero Gauss-Bonnet coupling of either sign can lead to a pointwise violation of the Quantum Focusing Conjecture. This violation is due to the classical geometric terms appearing in the QFC. Since those geometric terms are properly understood as expectation values of operators in an effective field theory, we argue that they are only well-defined when smeared over a region at least as large as the cutoff scale of the theory (which may be the Planck scale). We find that this smearing prescription removes the pointwise violation found by Fu et al.. We comment on the relationship to similar issues encountered in the study of Entanglement Wedge Nesting in holography.