  In the decoupling limit, the DGP model reduces to the theory of a scalar
field pi, with interactions including a specific cubic self-interaction - the
galileon term. This term, and its quartic and quintic generalizations, can be
thought of as arising from a probe 3-brane in a 5-dimensional bulk with
Lovelock terms on the brane and in the bulk. We study multi-field
generalizations of the galileon, and extend this probe brane view to higher
co-dimensions. We derive an extremely restrictive theory of multiple galileon
fields, interacting through a quartic term controlled by a single coupling, and
trace its origin to the induced brane terms coming from Lovelock invariants in
the higher co-dimension bulk. We explore some properties of this theory,
finding de Sitter like self accelerating solutions. These solutions have ghosts
if and only if the flat space theory does not have ghosts. Finally, we prove a
general non-renormalization theorem: multi-field galileons are not renormalized
quantum mechanically to any loop in perturbation theory.
