The energy and stability of D-term strings

TL;DR

This paper proves the non-perturbative stability of positive deficit angle D-term strings in supergravity using energy theorems, while highlighting the pathological nature of negative deficit angle strings that violate energy conditions.

Contribution

It demonstrates the stability of supersymmetric D-term strings via a positive energy theorem and clarifies the issues with negative deficit angle strings.

Findings

Positive deficit angle D-term strings are non-perturbatively stable.

Negative deficit angle D-term strings violate energy conditions and are pathological.

Witten-Nester charge computes gravitational energy without a cut-off.

Abstract

Cosmic strings derived from string theory, supergravity or any theory of choice should be stable if we hope to observe them. In this paper we consider D-term strings in D=4, N=1 supergravity with a constant Fayet-Iliopoulos term. We 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. Particular attention is paid to the negative deficit angle D-term string, which is known to violate the dominant energy condition. Within the class of string solutions we consider, this violation implies that the negative deficit angle D-term string must have a naked pathology and therefore the positive energy theorem we prove does not apply to it. As an interesting aside, we show that the Witten-Nester charge calculates the total gravitational energy of the D-term string without the need for a cut-off, which may not have been expected.