Violating the quantum focusing conjecture and quantum covariant entropy bound in d >= 5 dimensions

摘要

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 >= 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 >= 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 <= 4 spacetime dimensions remains open.