  The DBI and special galileon theories exhibit a conformal symmetry at
unphysical values of the spacetime dimension. We find the Lagrangian form of
this symmetry. The special conformal transformations are non-linearly realized
on the fields, even though conformal symmetry is unbroken. Commuting the
conformal transformations with the extended shift symmetries, we find new
symmetries, which when taken together with the conformal and shift symmetries
close into a larger algebra. For DBI this larger algebra is the conformal
algebra of the higher dimensional bulk in the brane embedding view of DBI. For
the special galileon it is a real form of the special linear algebra. We also
find the Weyl transformations corresponding to the conformal symmetries, as
well as the necessary improvement terms to make the theories Weyl invariant, to
second order in the coupling in the DBI case and to lowest order in the
coupling in the special galileon case.
