  In this note, which is based on hep-th/0611111, we review the stability of
the static, positive deficit angle D-term string solutions of D=4, N=1
supergravity with a constant Fayet-Iliopoulos term. We prove the semi-classical
stability of this class of solutions using standard positive energy theorem
techniques. In particular, we discuss how the negative deficit angle D-term
string, which also solves the Killing spinor equations, violates the dominant
energy condition and so is excluded from our arguments.
