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

In this paper we will consider quantum aspects of a non-local, infinite-derivative scalar field theory-a 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 asymptotically free, thus providing strong prospects of resolving various classical and quantum divergences. In particular, we will find that at one loop, the two-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet behavior of all other one-loop diagrams as well as the two-loop, two-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.