Generalized ghost-free propagators in nonlocal field theories

In this talk I introduce nonlocal (infinite derivative) field theories. First of all, I discuss how and which principles of quantum field theory are affected when higher-order derivative operators are taken into account in a Lagrangian. In particular, I focus on the issue of unitarity and on how to make higher-derivative theories healthy by means of non-polynomial differential operators. I present an iterative method to generate an infinite class of novel nonlocal field theories whose propagators are ghost-free. I first examine the scalar field case and show that the propagator pole structure can also contain additional pairs of complex conjugate poles which, however, do not spoil tree-level unitarity. Subsequently, I extend the same treatment to the gravity sector and consider nonlocal theories whose graviton propagators are ghost-free, and explore the possibility of regularizing singularities in these theories. This talk is mainly based on: arXiv:2001.07830, Phys.Rev. D 101, 084019 (2020).