Violating the Quantum Focusing Conjecture and Quantum Covariant Entropy Bound in $d\ge 5$ dimensions

We study the Quantum Focussing Conjecture (QFC) in curved spacetime. Noting that quantum corrections from integrating out massive fields generally induce a Gauss-Bonnet term, we study Einstein-Hilbert-Gauss-Bonnet gravity and show for $d\ge 5$ spacetime dimensions that weakly-curved solutions can violate the associated QFC for either sign of the Gauss-Bonnet coupling. The nature of the violation shows that -- so long as the Gauss-Bonnet coupling is non-zero -- it will continue to arise for local effective actions containing arbitrary further higher curvature terms, and when gravity is coupled to generic $d\ge 5$ theories of massive quantum fields. The argument also implies violations of a recently-conjectured form of the generalized covariant entropy bound. The possible validity of the QFC and covariant entropy bound in $d\le 4$ spacetime dimensions remains open.