Transmutation of nonlocal scale in infinite derivative field theories

Understand

In this paper we will show an ultraviolet -infrared connection for ghost-free infinite derivative field theories where the Lagrangians are made up of exponentials of entire functions.

• In particular, for $N$-point amplitudes a new scale emerges in the infrared from the ultraviolet, i.e.
• $M_{\rm eff}\sim M_s/N^\alpha,$ where $M_s$ is the fundamental scale beyond the Standard Model, and $\alpha>0$ depends on the specific choice of an entire function and on whether we consider zero or nonzero external momenta.
• We will illustrate this by first considering a scalar toy model with a cubic interaction, and subsequently a scalar toy-model inspired by ghost-free infinite derivative theories of gravity.