Twisted Covariant Noncommutative Self-dual Gravity

TL;DR

This paper develops a twisted covariant framework for noncommutative self-dual gravity, solving torsion at all orders and deriving the first-order expansion of the Plebański action in noncommutative geometry.

Contribution

It introduces a novel twisted covariant formulation for noncommutative self-dual gravity and explicitly computes the first-order $ heta$-expansion of the Plebański action.

Findings

Noncommutative torsion is solved at all orders in $ heta$.

First-order $ heta$-expansion of the Plebański action is explicitly derived.

Framework connects twisted noncommutative gauge theories with gravity.

Abstract

A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the $\theta$-expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in $\theta$ for the Pleba\'nski action is explicitly obtained.