All Physics Faculty Publications

Document Type

Contribution to Book

Journal/Book Title/Conference

Contemporary Mathematics

Volume

132

Editor

M. Gotay, J. Marsden, V. Moncrief

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.

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.

http://arxiv.org/abs/hep-th/9109034

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