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arXiv · 2004.09214

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

Subhash Mahapatra
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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 $\alpha\rightarrow\alpha/(D-4)$. 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 $D\rightarrow4$ 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.

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Subhash Mahapatra. 2020-04-20. A note on the total action of $4D$ Gauss-Bonnet theory. https://doi.org/10.1140/epjc%2Fs10052-020-08568-6

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