Abstract
It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity is renormalizable in D=2. This is where the research in the field of two derivatives theories is currently standing. We hereby present a class of weakly non-local higher derivative gravitational and gauge theories universally consistent at quantum level in any spacetime dimension. These theories are unitary (ghost-free) and perturbatively renormalizable. Moreover, we can always find a simple extension of these theories that is super-renormalizable or finite at quantum level in even and odd spacetime dimensions. Finally, we propose a super-renormalizable or finite theory for gravity coupled to matter laying the groundwork for a "finite standard model of particle physics" and/or a grand unified theory of all fundamental interactions.
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