​Super-Renormalizable Quantum Gravity

Besides non-local theories we propose another ultraviolet completion of the Einstein's gravity compatible with unitarity and super-renormalizability or finiteness. These gravitational theories are local, but the special structure of the operators quadratic in the Riemann tensor allows for only the usual real graviton pole in k^2=0 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 (CLOP) for the construction of a unitary S-matrix. Therefore, the spectrum consists on the graviton and short lived elementary unstable particles that we could name "anti-gravitons" because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs may be proposed, 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 can be interpreted as a white hole precursor. Consistently with the 't Hooft complementarity 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.  We recently computed the beta-fuctions for the Newton and cosmological constant, while the last two beta functions for R^2 and          are not an easy task, but we will surely calculate them in the upcoming years. 

 

We can extend the ideas implemented for gravity to all the other fundamental interactions to get a new super-reneromalizable or finite Lee-Wick standard model of particle physics. The properties of these theories will be investigated in future work with particular attention to the experimental constrains and eventual predictions. 

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