Vortices in Theories with Flat Directions

TL;DR

The paper investigates how flat directions in supersymmetric theories with FI D-terms induce a vacuum selection effect for vortex solutions, arguing that the selected vacuum minimizes the vector boson mass $m_v$ at the core. Using Bogomol'nyi techniques, it first recaps the known selection in simple Abelian models and then extends to $N=2$ SQED with two opposite-charge hypermultiplets, where BPS vortices become semilocal with a one-parameter width controlled by a zero mode, causing magnetic flux to spread and preventing confinement. The key finding is that, although the Bogomol'nyi bound is saturated, the presence of a neutral zero mode leads to arbitrarily wide, neutrally stable flux tubes, suppressing vorton production cosmologically and undermining certain magnetic confinement scenarios inspired by Calabi–Yau compactifications. This work provides a general criterion for vacuum selection in equal-charge Abelian theories and highlights differences arising when charges are not equal, with implications for string-inspired cosmology and vortex dynamics.

Abstract

In theories with flat directions containing vortices, such as supersymmetric QED, there is a vacuum selection effect in the allowed asymptotic configurations. We explain the role played by gauge fields in this effect and give a simple criterion for determining what vacua will be chosen, namely those that minimise the vector mass. We then consider the effect of vacuum selection on stable (BPS) non-topological vortices in a simple Abelian model with N=2 supersymmetry which occurs as a low energy limit of Calabi-Yau compactifications of type II superstrings. In this case the magnetic flux spreads over an arbitrarily large area. We discuss the implications for cosmology and for superstring inspired magnetic confinement scenarios.