Renormalizability inD-dimensional higher-order gravity

Abstract

A simple expression for calculating the classical potential concerning D-dimensional gravitational models is obtained through a method based on the generating functional. The prescription is then used as a mathematical tool to probe the conjecture that renormalizable higher-order gravity models -which are, of course, nonunitary -are endowed with a classical potential that is nonsingular at the origin. It is also shown that the converse of this statement is not true, which implies that the finiteness of the classical potential at the origin is a necessary but not a sufficient condition for the renormalizability of the model. The systems we have utilized to verify the conjecture were fourthand sixth-order gravity models in D-dimensions. A discussion about the polemic question related to the renormalizability of new massive gravity, which Oda claimed to be renormalizable in 2009 and three years late was shown to be nonrenormalizable by Muneyuki and Ohta, is considered. We remark that the solution of this issue is straightforward if the aforementioned conjecture is employed. We point out that our analysis is restricted to local models in which the propagator has simple and real poles.

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

“…We have seen that the fourth-derivative gravity is not a healthy theory because of a massive ghost tensor that violates the unitarity at the tree level. Recently, it was confirmed that renormalizable higher-derivative gravities are nonunitary [6]. Hence, the ghost problem is not a relevant issue in this work.…”

“…Bilinearizing the Lagrangian in Eq. (1) together with imposing the de Donder gauge of [6]. Inverting O, one obtains the propagator for the fourth-derivative gravity…”

“…It was proven that the action (10) becomes super-renormalizable because the superficial divergence δ[= 4 + E − ∞ n=3 (n − 2)V n ] decreases as the number of vertices V n increases [4,6]. An important point to be reminded is that the same order of the last two six-derivative terms in (10) is a key to guarantee the renormalizability.…”

“…Recently, it was conjectured that the reverse of the above statement is not true, which indicates that the finiteness of the Newtonian potential at the origin is a necessary but not sufficient condition for the renormalizability of the model [4,5]. The model used in [5,6] includes a massive ghost tensor, massive ghost and heathy scalars in addition to a healthy tensor. Even though the potential is finite at r = 0, it is non-renormalizable by power counting.…”

Interesting Examples of Violation of the Classical Equivalence Principle but Not of the Weak One

“…Higher-derivative gravity is the only model that is known to be renormalizable along its matter couplings up to now [30]. Nonetheless, since this system is renormalizable, it is compulsorily nonunitary [31,32]. We call attention to the fact that the breaking down of unitarity is indeed a serious problem.…”