Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle

TL;DR

This paper develops a background-independent noncommutative gravity model using Fedosov deformation quantization, where the noncommutative fields are dynamical, leading to a covariant and background-independent theory with a new action for general relativity.

Contribution

It introduces a novel noncommutative gravity framework based on Fedosov quantization with dynamical noncommutative fields, and connects it to a new action for classical general relativity.

Findings

The model is coordinate covariant and background independent.

Noncommutative fields are dynamical, including symplectic form and connection.

A new action for classical general relativity emerges as a limit.

Abstract

Model of noncommutative gravity is constructed by means of Fedosov deformation quantization of endomorphism bundle. The fields describing noncommutativity -- symplectic form and symplectic connection -- are dynamical, and the resulting theory is completely coordinate covariant and background independent. Its interpretation in terms of Seiberg-Witten map is provided. Also, new action for ordinary (commutative) general relativity is given, which in the present context appears as a commutative limit of noncommutative theory.