  We present a new general class of four-dimensional effective field theories
with interesting global symmetry groups. These theories arise from purely
gravitational actions for (3+1)-dimensional branes embedded in higher
dimensional spaces with induced gravity terms. The simplest example is the well
known Galileon theory, with its associated Galilean symmetry, arising as the
limit of a DGP brane world. However, we demonstrate that this is a special case
of a much wider range of theories, with varying structures, but with the same
attractive features such as second order equations. In some circumstances,
these new effective field theories allow potentials for the scalar fields on
curved space, with small masses protected by non-linear symmetries. Such models
may prove relevant to the cosmology of both the early and late universe.
