Tachyon condensation and universality of DBI action
  We show that a low-energy action for massless fluctuations around a tachyonic soliton background representing a codimension one D-brane coincides with the Dirac-Born-Infeld action. The scalar modes which describe transverse oscillations of the D-brane are translational collective coordinates of the soliton. The appearance of the DBI action is a universal feature independent of details of a tachyon effective action, provided it has the structure implied by the open string sigma model partition function. 
G. Arutyunov, S. Frolov, S. Theisen and A.A. Tseytlin