  The tachyon effective field theory describing the dynamics of a non-BPS
D-brane in superstring theory has an infinitely thin but finite tension kink
solution describing a codimension one BPS D-brane. We study the world-volume
theory of massless modes on the kink, and show that the world volume action has
precisely the Dirac-Born-Infeld (DBI) form without any higher derivative
corrections. We generalize this to a vortex solution in the effective field
theory on a brane-antibrane pair. As in the case of the kink, the vortex is
infinitely thin, has finite energy density, and the world-volume action on the
vortex is again given exactly by the DBI action on a BPS D-brane. We also
discuss the coupling of fermions and restoration of supersymmetry and
$\kappa$-symmetry on the world-volume of the kink. Absence of higher derivative
corrections to the DBI action on the soliton implies that all such corrections
are related to higher derivative corrections to the original effective action
on the world-volume of a non-BPS D-brane or brane-antibrane pair.
