Alternative Self-dual Gravity in Eight Dimensions

TL;DR

This paper introduces an alternative formulation of self-dual gravity in eight dimensions using a MacDowell-Mansouri framework, connecting it to Einstein-Hilbert and Lovelock actions.

Contribution

It develops a novel eight-dimensional self-dual gravity formalism based on a MacDowell-Mansouri approach, linking it to known gravitational actions.

Findings

The action includes linear, quadratic, and cubic curvature terms.

The linear term reduces to the Einstein-Hilbert action with a cosmological constant.

The reduced action is equivalent to the Lovelock action in eight dimensions.

Abstract

We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell-Mansouri physical framework and a self-dual curvature symmetry we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein-Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions.