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

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