Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity

TL;DR

This paper investigates the quantum behavior of a non-local, infinite-derivative scalar field theory as a simplified model for quantum gravity, showing that its UV divergences can be controlled through renormalization, indicating promising avenues for resolving quantum gravity issues.

Contribution

It demonstrates that a covariant infinite-derivative gravity extension can have manageable UV behavior at one-loop after renormalization, suggesting potential for consistent quantum gravity models.

Findings

One-loop 2-point function remains divergent but is renormalizable.

Post-renormalization, higher-loop diagrams exhibit controlled UV behavior.

The approach may be extendable to arbitrary loop orders.

Abstract

In this paper we will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a $\it toy \, model$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it $\it asymptotically \, free$, thus providing strong prospects of resolving various classical and quantum divergences. In particular, we will find that at $1$-loop, the $2$-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet (UV) behavior of all other $1$-loop diagrams as well as the $2$-loop, $2$-point function remains well under control. We will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.