Topological Symmetries of Twisted N=2 Chiral Supergravity in Ashtekar Formalism

TL;DR

This paper explores a topological gravity theory on four-manifolds using Ashtekar formalism, establishing equivalence with existing models and offering new insights into gravitational instantons and intersection theory.

Contribution

It demonstrates the equivalence of a topological gravity model in Ashtekar formalism with existing models, providing a new approach to study gravitational instantons.

Findings

Established formal equivalence with Anselmi and Fre's topological gravity

Introduced a new method for analyzing intersection theory of gravitational instantons

Provided a framework for studying topological gravity via (3+1) decomposition

Abstract

In this paper a topological theory of gravity is studied on a four-manifold using the formalism of Capovilla {\sl et al}. We show that it is fact equivalent to Anselmi and Fre's topological gravity using the topological symmetries. Using this formalism gives us a new way to study topological gravity and the intersection theory of gravitational instantons if the (3+1) decomposition with respect to local coordinates is performed.