D-term strings

TL;DR

This work shows that in $d=4$, $N=1$ supergravity with a constant Fayet–Iliopoulos term, the local BPS cosmic string arising from a D-term potential preserves half of the supersymmetry, and it establishes a direct link between D-term strings and string-theory D$_1$-strings. By deriving the Killing spinor equations and Bogomol'nyi bounds, it demonstrates that F-term strings cannot be BPS in this setup, while D-term strings saturate the bound with a positive deficit angle tied to the energy, $oldsymbol{μ_{ m string}}=2oldsymbol{π}|n|oldsymbol{\xi}$, and $M_P^2 oldsymbol{Δ}= oldsymbol{μ_{ m string}}$. The authors provide multiple consistency checks—tension matching with D-branes, RR-charge matching via an axion dual, and the appearance of a gauged $R$-symmetry—supporting a conjecture that D$_1$-strings are described by D-term strings in the low-energy supergravity. They further discuss implications for brane–anti-brane systems, tachyon dynamics, and the form of the tachyon superpotential, framing the inter-brane potential as a one-loop renormalization of D-term energy. Overall, the paper builds a concrete bridge between four-dimensional supergravity solitons and string-theory D-strings, with potential impact on the understanding of non-BPS backgrounds and SUSY breaking mechanisms.

Abstract

We study the embedding of cosmic strings, related to the Abrikosov-Nielsen-Olesen vortex solution, into d=4, N=1 supergravity. We find that the local cosmic string solution which saturates the BPS bound of supergravity with $D$-term potential for the Higgs field and with constant Fayet--Iliopoulos term, has 1/2 of supersymmetry unbroken. We observe an interesting relation between the gravitino supersymmetry transformation, positive energy condition and the deficit angle of the cosmic string. We argue that the string solutions with magnetic flux with F-term potential cannot be supersymmetric, which leads us to a conjecture that D1-strings (wrapped D(1+q)-branes) of string theory in the effective 4d supergravity are described by the D-term strings that we study in this paper. We give various consistency checks of this conjecture, and show that it highlights some generic properties of non-BPS string theory backgrounds, such as brane-anti-brane systems. Supersymmetry breaking by such systems can be viewed as FI D-term breaking, which implies, under certain conditions, the presence of gauged R-symmetry on such backgrounds. The D-term nature of the brane-anti-brane energy can also provide information on the superpotential for the tachyon, which Higgses the R-symmetry. In this picture, the inter-brane force can be viewed as a result of the world-volume gauge coupling renormalization by the open string loops.