Graviton partial waves and causality in higher dimensions

Abstract

Do gravitational interactions respect the basic principles of relativity and quantum mechanics? We show that any graviton $S$-matrix that satisfies these assumptions cannot significantly differ from General Relativity at low energies. We provide sharp bounds on the size of potential corrections in terms of the mass $M$ of new higher-spin states, in spacetime dimensions $D\ensuremath{\ge}5$ where the $S$-matrix does not suffer from infrared ambiguities. The key novel ingredient is the full set of $\mathrm{SO}(D\ensuremath{-}1)$ partial waves for this process, which we show how to efficiently compute with Young tableau manipulations. We record new bounds on the central charges of holographic conformal theories.