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

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arxiv 2004.09214 v2 pith:3QS3YSR7 submitted 2020-04-20 gr-qc hep-th

Subhash Mahapatra This is my paper · ORCID
classification gr-qchep-th
keywords theoryactiongauss-bonnetalphalevellimitingon-shellsurface
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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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Cited by 4 Pith papers

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