  Recent developments in string inspired models of inflation suggest that
D-strings are formed at the end of inflation. Within the supergravity model of
D-strings there are 2(n-1) chiral fermion zero modes for a D-string of winding
n. Using the bounds on the relic vorton density, we show that D-strings with
winding number n>1 are more strongly constrained than cosmic strings arising in
cosmological phase transitions. The D-string tension of such vortons, if they
survive until the present, has to satisfy 8\pi G_N \mu \lesssim p 10^{-26}
where p is the intercommutation probability. Similarly, D-strings coupled with
spectator fermions carry currents and also need to respect the above bound.
D-strings with n=1 do not carry currents and evade the bound. We discuss the
coupling of D-strings to supersymmetry breaking. When a single U(1) gauge group
is present, we show that there is an incompatibility between spontaneous
supersymmetry breaking and cosmic D-strings. We propose an alternative
mechanism for supersymmetry breaking, which includes an additional U(1), and
might alleviate the problem. We conjecture what effect this would have on the
fermion zero modes.
