Quantum Loops in Non-Local Gravity

TL;DR

This paper explores quantum properties of a non-local scalar field theory as a simplified model for infinite-derivative gravity, showing potential for resolving divergences and maintaining control over quantum corrections.

Contribution

It demonstrates that a non-local, ghost-free scalar toy model of gravity can be renormalized at one-loop and possibly extended to higher loops, improving UV behavior.

Findings

One-loop 2-point function remains divergent but can be renormalized.

Post-renormalization, higher-loop diagrams are well-behaved in the UV.

Potential generalization of the approach to arbitrary loop orders.

Abstract

In this proceedings, I 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, I 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. I will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.