A Deformation Theory of Self-Dual Einstein Spaces

Details A Deformation Theory of Self-Dual Einstein Spaces A Deformation Theory of Self-Dual Einstein Spaces

1991-09-20

arxiv.org/abs/hep-th/9109034v1

Contemp.Math. 132 (1991) 611

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

The self-dual Einstein equations on a compact Riemannian 4-manifold can be expressed as a quadratic condition on the curvature of an $SU(2)$ (spin) connection which is a covariant generalization of the self-dual Yang-Mills equations. Local properties of the moduli space of self-dual Einstein connections are described in the context of an elliptic complex which arises in the linearization of the quadratic equations on the $SU(2)$ curvature. In particular, it is shown that the moduli space is discrete when the cosmological constant is positive; when the cosmological constant is negative the moduli space can be a manifold the dimension of which is controlled by the Atiyah-Singer index theorem.

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