Physics of trans-Planckian gravity

Abstract

We study the field theoretical description of a generic theory of gravity flowing to Einstein general relativity in IR. We prove that, if ghost-free, in the weakly-coupled regime such a theory can never become weaker than general relativity. Using this fact, as a by-product, we suggest that in a ghost-free theory of gravity trans-Planckian propagating quantum degrees of freedom cannot exist. The only physical meaning of a trans-Planckian pole is the one of a classical state (black hole) which is described by the light IR quantum degrees of freedom and gives exponentially-suppressed contributions to virtual processes. In this picture Einstein gravity is UV self-complete, although not Wilsonian, and sub-Planckian distances are unobservable in any healthy theory of gravity. We then finally show that this UV/IR correspondence puts a severe constraint on any attempt of conventional Wilsonian UV-completion of trans-Planckian gravity. Specifically, there is no well-defined energy domain in which gravity could become asymptotically weak or safe.