Cosmic strings derived from string theory, supergravity or any theory of choice should be stable if we hope to observe them. The stability of solutions of supersymmetric theories is often inferred by considered linearised perturbations of the `BPS’-equations, however this is only consistent within a restricted class of symmetric perturbations. In this talk I will focus on D-term strings in D=4, N=1 supergravity with a constant Fayet-Iliopoulos term. I will show that the positive deficit angle supersymmetric D-term string is non- perturbatively stable by using standard Witten-Nester techniques to prove a positive energy theorem. An important point, which is often overlooked in such stability arguments, is the possible existence of negative energy solutions. I will discuss the negative deficit angle D-term string, which solves the supersymmetry conditions but is known to violate the dominant energy condition. I will show that within the class of string solutions I consider, this violation implies that the negative deficit angle D-term string must have a naked pathology and therefore the positive energy theorem does not apply to it. This means that it is possible to successfully complete the semi-classical positive energy theorem proof and reproduce the full Bogomol’nyi bound for the D-term string, proving it is stable.

Institute for Theoretical Physics, K.U. Leuven, Belgium