Solving the Riddle of the Incompatibility Between Renormalizability and Unitarity in N-Dimensional Einstein Gravity Enlarged by Curvature-Squared Terms

Abstract

One of the puzzling aspects of N-dimensional Einstein Gravity (NDEG) augmented by curvature-squared terms is why renormalizability and unitarity, two of the most important properties of any physical theory, cannot be reconciled in its framework. Actually, the reason why these properties are mutually incompatible within the context of generic higher-derivative models, not necessarily related to gravity, is one of the unsolved mysteries of physics. Here, a simple solution to the NDEG riddle, based on the analysis of the interparticle gravitational potential, is presented. The main argument used to support our discussion is that tree-level unitarity and the existence of a singularity in the potential are intertwined.

Weak-field limit and regular solutions in polynomial higher-derivative gravities

“…[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] and references therein. question of whether there is a fundamental relation between them [43,44,53]. The negative to this conjecture was given in [45], where it was shown that the Newtonian singularity is canceled in all the polynomial gravity theories with at least one massive mode in each sector, which included Lee-Wick and also some nonrenormalizable models.…”

“…This includes local superrenormalizable models and a wide class of Lee-Wick gravities. Following the aforementioned parallel between quantum and classical singularities [43][44][45]53], one can say that GR is nonrenormalizable and has a divergent Newtonian potential, fourth-order gravity is renormalizable and has a finite gravitational potential (but its curvature invariants diverge), and the higher-order gravities which are superrenormalizable have a complete regular nonrelativistic limit, i.e., the metric potentials and the curvatures have no singularities.…”

Stability issues of black hole in non-local gravity

“…It turns out that the infinite derivative gravity (non-local gravity) is ghostfree and renormalizable around the Minkowski spacetime background when one chooses the exponential form of an entire function [1,2]. We note that renormalizability can be easily checked by showing the finiteness of the Newtonian potential at the origin from the propagator [3,4,5,6].…”

Renormalizability, van Dam-Veltman-Zakharov discontinuity, and Newtonian singularity in higher-derivative gravity

“…The N = 0[N = 1] model corresponds to the fourth-derivative gravity (1) [sixth-derivative gravity (10)] with different coefficients. It requires that the two polynomials of F 1 and F 2 be of the same order.…”

“…Explicitly, there is a conjecture that renormalizable higher-derivative gravity has a finite Newtonian potential at the origin [1,2]. This relation was first notified in Stelle's seminal work [3] which showed that the fourth-derivative gravity is renormalizable, nonunitary and has a finite potential at origin.…”