Asymptotically nonlocal gravity

TL;DR

This paper extends the concept of asymptotically nonlocal field theories to linearized gravity, demonstrating an emergent regulator scale that resolves singularities and regulates quantum corrections, bridging Lee-Wick theories and nonlocal gravity.

Contribution

It generalizes asymptotically nonlocal constructions to linearized gravity and shows the emergence of a regulator scale in classical and quantum gravitational contexts.

Findings

The regulator scale resolves the singularity at the origin of a point particle's metric.

It modifies the nonrelativistic gravitational potential to include the regulator.

The scale regulates the one-loop graviton contribution to scalar field self-energy.

Abstract

Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymptotically nonlocal scalar, Abelian, and non-Abelian gauge theories has demonstrated the existence of an emergent regulator scale that is hierarchically smaller than the lightest Lee-Wick partner, in a limit where the Lee-Wick spectrum becomes dense and decoupled. We generalize this construction to linearized gravity, and demonstrate the emergent regulator scale in three examples: by studying the resolution of the singularity (i) at the origin in the classical solution for the metric of a point particle, and (ii) in the nonrelativistic gravitational potential computed via a one-graviton exchange amplitude; (iii) we also show how this derived scale regulates the one-loop graviton contribution to the self energy of a real scalar field. We comment briefly on the generalization of our approach to the full, nonlinear theory of gravity.