A note on the total action of 4D Gauss–Bonnet theory

Abstract

Recently, a novel four-dimensional Gauss–Bonnet theory has been suggested as a limiting case of the original D-dimensional theory with singular Gauss–Bonnet coupling constant α→ α/ (D- 4). The theory is proposed at the level of field equations. Here we analyse this theory at the level of action. We find that the on-shell action and surface terms split into parts, one of which does not scale like (D- 4). The limiting D→ 4 procedure, therefore, gives unphysical divergences in the on-shell action and surface terms in four dimensions. We further highlight various issues related to the computation of counterterms in this theory.