Super-renormalizable or Finite Lee-Wick Quantum Gravity

TL;DR

This paper introduces a super-renormalizable or finite multidimensional higher derivative gravity theory with complex conjugate poles, ensuring unitarity and potentially describing black hole precursors, with implications for quantum gravity and particle physics.

Contribution

It presents a novel class of higher derivative gravity theories that are super-renormalizable or finite, incorporating Lee-Wick prescriptions and complex poles to maintain unitarity and address quantum gravity issues.

Findings

The theory is super-renormalizable in even dimensions.

The theory is finite in odd dimensions.

A singularity-free Newtonian potential is derived.

Abstract

We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee-Wick and Cutkoski, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists on the graviton and short lived elementary unstable particles that we named "anti-gravitons" because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the complex conjugate of the micro black hole precursor has received as a white hole precursor consistently with the t'Hooft complementary principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-reneromalizable or finite Lee-Wick standard model of particle physics.