Abstract
In this paper we present an iterative method to generate an infinite class of new nonlocal field theories whose propagators are ghost-free. We first examine the scalar field case and show that the pole structure of such generalized propagators possesses the standard two derivative pole and in addition can contain complex conjugate poles which, however, do not spoil at least tree level unitarity as the optical theorem is still satisfied. Subsequently, we define analogous propagators for the fermionic sector which is also devoid of unhealthy degrees of freedom. As a third case, we apply the same construction to gravity and define a new set of theories whose graviton propagators around the Minkowski background are ghost-free. Such a wider class also includes nonlocal theories previously studied, and Einstein's general relativity as a peculiar limit. Moreover, we compute the linearized gravitational potential generated by a static point-like source for several gravitational theories belonging to this new class and show that the nonlocal nature of gravity regularizes the singularity at the origin.
Highlights
Einstein’s general relativity (GR) has been the most successful theory of gravity so far; its predictions have been tested to very high precision in the infrared regime, i.e., at large distances and late times [1], though it still needs to be tested at cosmological scales
IV, we briefly review the main aspects of generalized quadratic curvature actions around the Minkowski background
In order to set up our framework, we review the main aspects of quadratic curvature gravity around flat spacetime
Summary
Einstein’s general relativity (GR) has been the most successful theory of gravity so far; its predictions have been tested to very high precision in the infrared regime, i.e., at large distances and late times [1], though it still needs to be tested at cosmological scales. First relevant applications of infinite derivative field theories in a gravitational context were made in Refs. The same construction can be performed in a gravitational context around the Minkowski background, where one can define a ghost-free nonlocal graviton propagator made up of the standard massless pole, p2 1⁄4 0, plus an infinite set of complex conjugate pairs.. We will present an iterative method to generate an infinite tower of nonlocal theories which preserves tree level unitarity despite possessing higher (infinite) order time derivatives. In the rest of the paper, we set M 1⁄4 1 for simplicity
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