A Universal Pattern in Quantum Gravity at Infinite Distance

TL;DR

This paper uncovers a universal pattern linking the variation rates of the quantum gravity cut-off and the lightest tower of states at infinite distance limits, refining Swampland criteria for effective field theories.

Contribution

It introduces a universal relation between the variation rates of the quantum gravity cut-off and the lightest mass tower at infinite distance limits in field space.

Findings

The relation holds in any spacetime dimension.

It constrains how the cut-off and lightest mass scale vary together.

It refines existing Swampland criteria for quantum gravity compatibility.

Abstract

Quantum gravitational effects become significant at a cut-off species scale that can be much lower than the Planck scale whenever we get a parametrically large number of fields becoming light. This is expected to occur at any perturbative limit of an effective field theory coupled to gravity, or equivalently, at any infinite distance limit in the field space of the quantum gravity completion. In this note, we present a universal pattern that links the asymptotic variation rates in field space of the quantum gravity cut-off $\Lambda_{\text{sp}}$ and the characteristic mass of the lightest tower of states $m$: $\frac{\vec\nabla m}{m} \cdot\frac{\vec\nabla \Lambda_{\rm sp}}{ \Lambda_{\rm sp}}=\frac1{d-2}$, where $d$ is the spacetime dimension. This restriction can be used to make more precise several Swampland criteria that constrain the effective field theories that can be consistently coupled to quantum gravity.