Quantum gravity constraints from unitarity and analyticity

We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In D >= 4 spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in D = 4 and D = 5 before extending to D >= 6. Afterwards, we derive positivity bounds for super-symmetric 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 D >= 5 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.