2020/04/30 by James Bonifacio, Kurt Hinterbichler, Laura A. Johnson · 1 citation
Physics and Astronomy · #hep-th #gr-qc
paper · pdf · doi:10.1103/physrevd.102.024029
published as Phys. Rev. D 102, 024029 (2020) · 18 pages
arxiv created 2020/07/09 · arxiv updated 2020/07/15
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 (∂ϕ)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.