  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.
