The $L_{\infty}$-structure of noncommutative gravity

TL;DR

This paper explores the structure of noncommutative gravity using homotopy algebras, introducing braided gauge symmetries and proposing a new four-dimensional noncommutative gravity theory within the Einstein-Cartan-Palatini framework.

Contribution

It presents a novel approach to noncommutative gravity by employing homotopy algebra perspectives and braided gauge symmetries, leading to a new four-dimensional theory.

Findings

Introduction of braided gauge symmetries in noncommutative field theories

Development of a new noncommutative gravity model in four dimensions

Application of homotopy algebra frameworks to gravity theories

Abstract

We summarise recent perspectives on symmetries of noncommutative field theories based on homotopy algebras. We show how these viewpoints naturally lead to a new class of noncommutative field theories which possess braided gauge symmetries, and explain in detail their uses in gravity. We review how these considerations lead to a new theory of noncommutative gravity in four dimensions within the Einstein-Cartan-Palatini formalism.