  A flat 3-brane probing a five dimensional anti-de Sitter space has the same
symmetries and symmetry breaking pattern as one probing a five dimensional de
Sitter space with two time directions. Despite the seemingly different physical
set ups, we show that the effective field theory of the brane bending mode is
identical in both cases. In particular, despite "wrong" signs in the DBI action
for the two-time de Sitter case, the theories have the same S-matrix. This is
consistent with the expectation that effective field theories are determined
solely by their degrees of freedom and pattern of symmetry breaking, even in
the case of spacetime symmetries. We comment further on the equivalence between
the Weyl/dilaton and DBI representations of the EFT of broken conformal
symmetry.
