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 $\alpha \to \alpha /(D-4)$. 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 $D\to 4$ 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.

15 pages; general discussion extended; typos corrected; references added. Published version

References in corpus (4)

• Black holes in the four-dimensional Einstein-Lovelock gravity
• Vacuum energy in Einstein-Gauss-Bonnet AdS gravity
• Counterterms in Dimensionally Continued AdS Gravity
• Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method

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