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

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.

20 pages, 5 figures

References in corpus (7)

• Black holes in an ultraviolet complete quantum gravity
• The causal set approach to quantum gravity
• Ultraviolet Complete Quantum Gravity
• Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
• Finite Temperature Solitons in Non-Local Field Theories from p-Adic Strings
• An introduction to quantum gravity
• Wald's gravitational entropy for ghost-free, infinite derivative theories of Gravity

Cited by in corpus (2)

• Slavnov Identities for Infinite Derivative Theory of Gravity
• Unitarity in Infinite Derivative Theories