  We give the equations of motion for a self-gravitating Dirac p-brane embedded
in an even co-dimension spacetime. The dynamics of the bulk are dictated by
Lovelock gravity and permit matching conditions, even when the codimension is
strictly greater than 2. We show that the equations of motion involve both
induced Lovelock densities on the brane and regular extrinsic curvature terms.
The brane dynamics can be derived from an exact (p+1)-dimensional induced
action. The Dirac charge is carried by an overall (solid) angle defect which
sets the Planck scale on the brane. In particular, if the codimension is
greater than the worldvolume dimension of the p-brane, we show that the
extrinsic curvature terms cancel, leaving an exact induced Lovelock theory. For
example, a 3-brane embedded in 8 or 10 dimensions obeys Einstein's equations
with a cosmological constant.
