  We consider F and D-term cosmic strings formed in supersymmetric theories.
Supersymmetry is broken inside the string core, but restored outside. In global
SUSY, this implies the existence of goldstino zero modes, and the string
potentially carries fermionic currents. We show that these zero modes do not
survive the coupling to gravity, due to the super Higgs mechanism. Therefore
the superconductivity and chirality properties are different in global and
local supersymmetry. For example, a string formed at the end of D-term
inflation is chiral in supergravity but non-chiral in global SUSY.
