Gauge and Einstein Gravity from Non-Abelian Gauge Models on Noncommutative Spaces

TL;DR

This paper develops a model of gauge gravity on noncommutative spaces using enveloping algebras and star product calculus, establishing conditions for equivalence to general relativity and defining dynamics via Seiberg-Witten maps.

Contribution

It introduces a novel formulation of gauge gravity on noncommutative spaces and constructs Seiberg-Witten maps to relate it to classical general relativity.

Findings

Formulated gauge gravity model on noncommutative spaces

Established Seiberg-Witten maps for gravitational fields

Analyzed conditions for equivalence to general relativity

Abstract

Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding Seiberg-Witten maps are established which allow the definition of respective dynamics for a finite number of gravitational gauge field components on noncommutative spaces.