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arXiv · 2004.10716

Amplitudes and 4D Gauss-Bonnet Theory

James Bonifacio·Kurt Hinterbichler·Laura A. Johnson
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Abstract

It has recently been argued that there may be a nontrivial four-dimensional limit of the higher-dimensional Gauss--Bonnet and Lovelock interactions and that this might provide a loophole allowing for new four-dimensional gravitational theories, possibly without a standard Lagrangian. We investigate this claim by studying tree-level graviton scattering amplitudes, allowing us to draw conclusions independently of the Lagrangian. By taking four-dimensional limits of higher-dimensional scattering amplitudes of the Gauss--Bonnet theory, we find four-dimensional amplitudes that are different from general relativity; however, these amplitudes are not new since they all come from certain scalar-tensor theories. The nontrivial limit that does not lead to infinite strong coupling around flat space leads to $(\partial\phi)^4$ theory. We argue that there cannot be any six-derivative purely gravitational four-point amplitudes in any dimension other than those coming from Lovelock theory by directly constructing the on-shell amplitudes. In particular, there can be no new such amplitudes in four dimensions beyond those of general relativity. We also present some new results on the spin-averaged cross section for graviton-graviton scattering in general relativity and Gauss--Bonnet theory in arbitrary dimensions.

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James Bonifacio, Kurt Hinterbichler, Laura A. Johnson. 2020-04-22. Amplitudes and 4D Gauss-Bonnet Theory. https://doi.org/10.1103/physrevd.102.024029

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