  We will construct a loop space formalism for general relativity, and
construct the Polyakov variables as connections for such a loop space. We will
use these Polyakov variables to construct a dual theory of gravity beyond
linear approximation. It will be demonstrated that this loop space duality
reduces to the Hodge duality for linearized gravity. Furthermore, a loop space
curvature will be constructed from this Polyakov variable. It will be shown
that this loop space curvature vanishes in the absence of topological defects,
and so it can be used to investigate gravitational monopoles. We will also
construct the suitable monopole charge for such gravitational monopoles.
