  The occurrence of singularities at the centers of black holes suggests that
general relativity (GR), although a highly successful model of gravity and
cosmology, is inapplicable. This is due to the breakdown of the equivalence
principle. Gauss-Bonnet (GB) action is a simplest extension of GR as it possess
second-order equations of motion and is devoid of ghosts. However, in 4-D, the
GB action is topological. Recently, Glavan and Lin proposed a mathematical
framework that transforms the 4-D GB gravity theory into a non-topological one.
However, it has been argued that without a canonical way to choose 4-D from the
higher-dimensional space, such a GB gravity is not well-defined in 4-D. The
current work takes a step in addressing this issue by demonstrating that the
rescaling of the GB coupling $\alpha \rightarrow \alpha/(D - 4)$ arises from
the self-energy correction of gravitons in 4-D via \emph{the dimensional
regularization}. To keep things transparent, we focus on the linearized theory
of gravity coupled with matter fields. By computing the one-loop self-energy
correction of gravitons induced by the matter fields, we explicitly provide the
origin of the prescription provided by Glavan and Lin. Our work naturally opens
a new window to considering 4-D Einstein Gauss-Bonnet gravity as the most
straightforward modification to GR.
