Finite 4-D Gauss-Bonnet quantum corrections from matter-graviton interactions in a curved background

Abstract

The Glavan-Lin proposal for 4D Einstein-Gauss-Bonnet (EGB) gravity introduces a singular dimensional scaling to bypass Lovelock's theorem, though its fundamental origin remains debated. In this work, we demonstrate that this specific dimension-dependent scaling naturally emerges from the one-loop self-energy corrections of gravitons. By employing real-space techniques to evaluate graviton interactions with minimally coupled scalar and electromagnetic fields in a de Sitter background, we show that the $1/(D-4)$ pole from dimensional regularization naturally yields a term proportional to the Gauss-Bonnet invariant. Importantly, because the Gauss-Bonnet density is a total derivative in four dimensions, this combination yields a strictly finite quantum correction analogous to the conformal anomaly, rather than a divergent counterterm. We confirm that the true ultraviolet divergences are strictly renormalized by standard quadratic curvature counterterms, specifically the Weyl-squared and Ricci-scalar-squared invariants. Our results indicate that the Glavan-Lin scaling is not an ad-hoc classical limit, but effectively captures a finite, loop-induced quantum feature of the effective action. We discuss the implications of these finite, background-dependent corrections in the early-Universe and their consequences in the strong gravity regime.