Universal Pattern in Quantum Gravity at Infinite Distance

Quantum gravitational effects become significant at a cutoff that can be much lower than the Planck scale whenever there is a large number of light fields. This is expected to occur at any perturbative limit of an effective field theory coupled to gravity, or equivalently, at infinite distance in the field space of the UV completion. In this note, we present a universal pattern that links the asymptotic variation in field space of the quantum gravity cutoff Λₒ₏ and the characteristic mass of the lightest tower of states m: (∇over →m/m) · (∇over →Λₒ₏/Λₒ₏) =1/ (d-2), with d the spacetime dimension. This restriction can be used to make more precise several Swampland criteria that constrain any effective field theory which can be consistently coupled to quantum gravity.