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

TL;DR

This paper addresses whether the Quantum Focussing Conjecture (QFC) remains valid when quantum corrections induce higher-curvature terms, focusing on the Gauss-Bonnet contribution in the Einstein-Hilbert-Gauss-Bonnet action. In $d \ge 5$ the authors show, in the weak-curvature regime, that the QFC can be violated for either sign of the Gauss-Bonnet coupling $\gamma$, with the violation controlled by a nonzero quantity $Q$ that depends on Weyl tensor components; this violation persists when additional higher-derivative terms are present and extends to semi-classical gravity with massive fields. They further argue that the same construction leads to violations of a recently conjectured generalized covariant entropy bound (quantum Bousso bound). The discussion highlights open questions for $d \le 4$ and suggests that effective-field-theory considerations, including a possibly scale-dependent QFC and the role of $R_{ab}R^{ab}$ terms, may be essential to reconciling these bounds with quantum corrections.

Abstract

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.