Abstract
We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in and before extending to . Afterwards, we derive positivity bounds for supersymmetric operators and verify that all of our constraints are satisfied by weakly coupled string theories. Among quadratic curvature operators, we find that the Gauss-Bonnet term in is inconsistent unless new degrees of freedom enter at the natural cutoff scale defined by the effective theory. Our bounds apply to perturbative ultraviolet completions of gravity.
- Received 5 January 2016
DOI:https://doi.org/10.1103/PhysRevD.93.064076
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