Towards an Ashtekar Formalism in Twelve Dimensions

TL;DR

This paper explores extending the Ashtekar formalism to twelve-dimensional spacetime, analyzing exceptional signatures 2+2 and 0+8 through self-dual actions, potentially broadening the formalism's applicability in higher dimensions.

Contribution

It introduces a framework for applying the Ashtekar formalism in twelve dimensions, focusing on exceptional signatures 2+2 and 0+8 via self-dual actions.

Findings

Both 2+2 and 0+8 signatures can be analyzed using self-dual Ashtekar actions.

The transition from 2+10 to (2+2)+(0+8) signatures is feasible within this formalism.

The approach opens pathways for higher-dimensional quantum gravity theories.

Abstract

We discuss the Ashtekar formalism from the point of view of twelve dimensions. We first focus on the 2+10 spacetime signature and then we consider the transition $2+10\to (2+2)+(0+8)$. We argue that both sectors 2+2 and 0+8, which are exceptional signatures, can be analyzed from the point of view of a self-dual action associated with the Ashtekar formalism.