Two-Connection Renormalization and Nonholonomic Gauge Models of Einstein Gravity

TL;DR

This paper introduces a novel approach to quantum gravity using nonholonomic geometry, reformulating Einstein gravity as a gauge model, and demonstrates two-loop renormalizability with reduced computational complexity.

Contribution

It develops a nonholonomic gauge model framework for Einstein gravity that achieves two-loop renormalization and simplifies quantum gravitational calculations.

Findings

Reformulation of Einstein gravity as a nonholonomic gauge model.

Two-loop renormalizability of the proposed quantum gravity model.

Reduction of calculation complexity to one- and two-loop levels.

Abstract

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:0902.0911 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 distortion 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.