Two-Connection Renormalization and Nonholonomic Gauge Models of Einstein Gravity

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.

latex2e, 40 pages, v4, accepted for Int. J. Geom. Meth. Mod. Phys. 7 (2010)

References in corpus (10)

• Loop Quantum Gravity: An Inside View
• Finsler and Lagrange Geometries in Einstein and String Gravity
• Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows
• Nonholonomic Ricci Flows: II. Evolution Equations and Dynamics
• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Deformation Quantization of Nonholonomic Almost Kahler Models and Einstein Gravity
• Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
• Parametric Nonholonomic Frame Transforms and Exact Solutions in Gravity
• Einstein Gravity as a Nonholonomic Almost Kahler Geometry, Lagrange-Finsler Variables, and Deformation Quantization
• Curve Flows in Lagrange-Finsler Geometry, Bi-Hamiltonian Structures and Solitons

Cited by in corpus (7)

• Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
• Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models
• Hidden Symmetries for Ellipsoid-Solitonic Deformations of Kerr-Sen Black Holes and Quantum Anomalies
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Covariant Renormalizable Anisotropic Theories and Off-Diagonal Einstein-Yang-Mills-Higgs Solutions
• Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories
• Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications