2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/180591In 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.9 pages, contribution to the proceedings of the RTN project `Constituents, Fundamental Forces and Symmetries of the Universe' conference in Napoli, October 9 - 13, 2006High Energy Physics - Theorytext