Gravitational Regge bounds
Abstract
We review the basic assumptions and spell out the detailed arguments that lead to the bound on the Regge growth of gravitational scattering amplitudes. The minimal extra ingredient compared to the gapped case  in addition to unitarity, analyticity, subexponentiality, and crossing  is the assumption that scattering at large impact parameters is controlled by known semiclassical physics. We bound the Regge growth of amplitudes both with the fixed transferred momentum and smeared over it. Our basic conclusion is that gravitational scattering amplitudes admit dispersion relations with two subtractions. For a subclass of smeared amplitudes, black hole formation reduces the number of subtractions to one. Finally, using dispersion relations with two subtractions we derive bounds on the local growth of relativistic scattering amplitudes. Schematically, the local bound states that the amplitude cannot grow faster than s^2s2. The results obtained in the paper are valid for d> 4d>4 for which the 2\to22→2 scattering amplitude is welldefined.
 Publication:

SciPost Physics
 Pub Date:
 January 2024
 DOI:
 10.21468/SciPostPhys.16.1.034
 arXiv:
 arXiv:2202.08280
 Bibcode:
 2024ScPP...16...34H
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology
 EPrint:
 17 pages + appendices, 9 figures