Cosmic D-strings as Axionic D-term Strings
  In this work we derive non-singular BPS string solutions from an action that captures the essential features of a D-brane-anti-D-brane system compactified to four dimensions. The model we consider is a supersymmetric abelian Higgs model with a D-term potential coupled to an axion-dilaton multiplet. The strings in question are axionic D-term strings which we identify with the D-strings of type II string theory. In this picture the Higgs field represents the open string tachyon of the D-Dbar pair and the axion is dual to a Ramond Ramond form. The crucial term allowing the existence of non-singular BPS strings is the Fayet-Iliopoulos term, which is related to the tensions of the D-string and of the parent branes. Despite the presence of the axion, the strings are BPS and carry finite energy, due to the fact that the space gets very slowly decompactified away from the core, screening the long range axion field (or equivalently the theory approaches an infinitely weak 4D coupling). Within our 4D effective action we also identify another class of BPS string solutions (s-strings) which have no ten dimensional analog, and can only exist after compactification. 
Jose J. Blanco-Pillado, Gia Dvali and Michele Redi