Towards UV Finiteness of Infinite Derivative Theories of Gravity and Field Theories

TL;DR

This paper demonstrates that in a ghost-free infinite-derivative scalar model inspired by gravity, all multi-loop, multi-point Feynman diagrams become UV finite and exhibit exponentially decreasing external momentum dependence at high loop orders.

Contribution

It proves UV finiteness of all 1PI Feynman diagrams in a ghost-free infinite-derivative scalar theory using dressed vertices and propagators, extending to arbitrary loop and point diagrams.

Findings

All n-loop, N-point diagrams are UV finite.

External momentum dependence decreases exponentially with loop order.

High loop order diagrams eliminate external momentum divergences.

Abstract

In this paper we will consider the ultraviolet (UV) finiteness of the most general one-particle irreducible ($1$PI) Feynman diagrams within the context of ghost-free, infinite-derivative scalar toy model, which is inspired from ghost free and singularity-free infinite-derivative theory of gravity. We will show that by using dressed vertices and dressed propagators, $n$-loop, $N$-point diagrams constructed out of lower-loop $2$- & $3$-point and, in general, $N_i$-point diagrams are UV finite with respect to internal and external loop momentum. Moreover, we will demonstrate that the external momentum dependences of the $n$-loop, $N$-point diagrams constructed out of lower-loop $2$- & $3$-point and, in general, $N_i$-point diagrams decrease exponentially as the loop-order increases and the external momentum divergences are eliminated at sufficiently high loop-order.