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 $$\alpha \rightarrow \alpha /(D-4)$$ α → α / ( D - 4 ) . The theory is proposed at the level of field equations. Her...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-020-08568-6 |
| Summary: | 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 $$\alpha \rightarrow \alpha /(D-4)$$ 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 $$(D-4)$$ ( D - 4 ) . The limiting $$D\rightarrow 4$$ 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. |
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| ISSN: | 1434-6044 1434-6052 |