Moduli Space of Topological 2-form Gravity

TL;DR

This paper introduces a topological formulation of 4D Euclidean Einstein gravity using anti-self-dual 2-forms and SU(2) connections, characterizing the moduli space of conformally self-dual Einstein manifolds and analyzing its properties.

Contribution

It presents a novel topological approach to 4D gravity focusing on the moduli space of conformally self-dual Einstein manifolds and computes the index of the associated elliptic complex.

Findings

Describes the moduli space of conformally self-dual Einstein manifolds.

Evaluates the index of the elliptic complex with a cosmological constant.

Provides a topological perspective on 4D Euclidean gravity.

Abstract

We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual 2-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual Einstein manifolds. In the presence of a cosmological constant, we evaluate the index of the elliptic complex associated with the moduli space.