General relativity as the surface action of a five-dimensional gauge theory

Abstract

We show that the action of euclidean general relativity is the surface term of a five-dimensional O(5) gauge theory, thus realizing Hawking's conjecture that the functional integral be restricted to compact manifolds without boundary. Our treatment of general relativity uncovers and exploits analogies with monopoles and instantons in the O(5) gauge theory. We review the metric-independent treatment of general relativity, its implications for the renormalizability of pure gravity and reexamine the positivity problem for the euclidean action. The new phenomenon of spontaneous dimensional reduction, by which a spatial manifold loses a dimension when a scalar field acquires a vacuum value, is described - an approach to higher dimensions distinct from the usual Kaluza-Klein approach. We propose a five-dimensional gauge field model with positive action - for which the surface action is that of general relativity - and explore some of its consequences.