Quantum Loops in Non-Local Gravity

Understand

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.