Locally Anisotropic Supergravity and Gauge Gravity on Noncommutative Spaces

TL;DR

This paper develops a geometric framework for locally anisotropic supergravity and gauge gravity on noncommutative spaces, utilizing anholonomic superframes, nonlinear connections, and star product calculus.

Contribution

It introduces a novel model of gauge la-gravity on noncommutative spaces with explicit Seiberg-Witten maps for finite gravitational gauge fields.

Findings

Established Seiberg-Witten maps for the model

Defined dynamics for finite gravitational gauge components

Proposed a geometric approach to noncommutative supergravity

Abstract

We outline the the geometry of locally anisotropic (la) superspaces and la-supergravity. The approach is backgrounded on the method of anholonomic superframes with associated nonlinear connection structure. Following the formalism of enveloping algebras and star product calculus we propose a model of gauge la-gravity on noncommutative spaces. The corresponding Seiberg-Witten maps are established which allow the definition of dynamics for a finite number of gravitational gauge field components on noncommutative spaces.