All Physics Faculty Publications
Document Type
Contribution to Book
Journal/Book Title/Conference
Contemporary Mathematics
Volume
132
Publisher
American Mathematical Society
Publication Date
1991
First Page
611
Abstract
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.
Recommended Citation
C.G. Torre, A deformation theory of self-dual Einstein spaces, Contemp. Math. 132:611, 1991.
http://arxiv.org/abs/hep-th/9109034
Comments
Originally published by the American Mathematical Society. This article appeared in Contemporary Mathematics. Author post-print available online through arXiv.org and through link above.