Dimensional Regularization of Topological Terms in Dilaton Gravity

TL;DR

This paper reviews the structure and formulations of topological terms in dilaton gravity, especially the Gauss-Bonnet term, and explores their applications in cosmology and topological materials.

Contribution

It provides a comprehensive review of the regularization of topological terms in dilaton gravity and their connections to EGB theories and conformal anomalies.

Findings

Analysis of conformal constraints around flat space

Comparison of local and nonlocal formulations of effective actions

Applications to topological materials under stress

Abstract

The possibility of evading Lovelock's theorem at $d=4$, via a singular redefinition of the dimensionless coupling of the Gauss-Bonnet term, has been extensively discussed in the cosmological context. The term is added as a quadratic contribution of the curvature tensor to the Einstein-Hilbert action, originating theories of "Einstein Gauss-Bonnet" (EGB) type. These studies are interlaced with those of the conformal anomaly effective action. We review some basic results concerning the structure of these actions, their conformal constraints around flat space and their relation to EGB theories. The local and nonlocal formulations of such effective actions are illustrated. This class of theories find applications in the seemingly unrelated context of topological materials, subjected to thermal and mechanical stress.