Two–Connection Renormalization and Nonholonomic Gauge Models of Einstein Gravity

A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two–loop renormalizable effective actions. We use a key result from our partner work arXiv: 0902.0970 that the classical Einstein gravity theory can be reformulated equivalently as a nonholonomic gauge model in the bundle of affine/de Sitter frames on pseudo–Riemannian spacetime. It is proven that (for a class of nonholonomic constraints and splitting of the Levi–Civita connection into a ”renormalizable” distinguished connection, on a base background manifold, and a gauge like distorsion tensor, in total space) a nonholonomic differential renormalization procedure for quantum gravitational fields can be elaborated. Calculation labor is reduced to one– and two–loop levels and renormalization group equations for nonholonomic configurations.