A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual two-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of conformally self-dual Einstein manifolds for a cosmological constant A # 0 case and an Einstein-Kahlerian manifold with the vanishing real first Chern class for A = 0. In the A # 0 case, we evaluate the index of the elliptic complex associated with the moduli space and calculate the partition function. We also clarify the moduli space and its dimension for A = 0 which are related to Plebansky's heavenly equations.PACS number(s): 04.50.th, 04.20.Jb

No 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. *

No abstract

No abstract