Revision 1

Accepted · first revision · record

Title: Prove high-energy growth bound for gravitational amplitudes from first principles
Plain: All positivity arguments assume that scattering amplitudes do not grow too fast at high energy. For gravity this growth limit is assumed, not proven.
Precise: Prove that the $2 \to 2$ amplitude of a consistent quantum gravity theory satisfies $M(s,t)/s^{2} \to 0\ \text{as}\ s \to \infty\ \text{at fixed}\ t < 0$ (so dispersion relations with two subtractions hold), using only unitarity, analyticity, crossing and polynomial or subexponential boundedness, in $D \ge 4$. Haring and Zhiboedov (2022) derived this bound with the extra assumption that scattering at large impact parameter is controlled by known semiclassical physics; justifying or removing that assumption, and handling $D = 4$ infrared divergences, is the open part.
Settled by: A proof of the $s^{2}$ bound from axioms that do not assume semiclassical large-impact-parameter behavior, or a counterexample amplitude.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: partially-resolved
Status note: The 2022 derivation rests on the semiclassical large-impact-parameter assumption.
Posed since: (empty)