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Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?

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arxiv 2004.03390 v3 pith:E2YZR4S6 submitted 2020-04-07 gr-qc hep-th

Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?

classification gr-qc hep-th
keywords dimensionstheoryeinstein-gauss-bonnetfouralwaysdefineddimensionalfour-dimensional
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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No! We show that the field equations of Einstein-Gauss-Bonnet theory defined in generic $D>4$ dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to $D=4$. Therefore, the recently introduced four-dimensional, novel, Einstein-Gauss-Bonnet theory does not admit an intrinsically four-dimensional definition as such it does not exist in four dimensions. The solutions (the spacetime, the metric) always remain $D>4$ dimensional. As there is no canonical choice of 4 spacetime dimensions out of $D$ dimensions for generic metrics, the theory is not well defined in four dimensions.

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