Vortices in theories with flat directions

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.

Flux tubes on Higgs branches in SUSY gauge theories

“…In ref. [15,16] vortices in N= 1 QED were considered and it was concluded that in generic point on the Higgs branch the string is unstable. The only vacuum which support string solutions is the base point of the Higgs branch <q >= 0.…”

“…The only vacuum which support string solutions is the base point of the Higgs branch <q >= 0. The so called "vacuum selection rule" was put forward in [15,16] to ensure this property. We would like to stress that our results here and in ref.…”

“…However, for vacua at the base S 2 cycle of the Eguchi-Hanson manifold for which quark VEV is equal to the FI-parameter ANO strings turn into semilocal strings [15,16]. For these vacua we have deconfinement phase.…”

“…Since then a lot of papers study confinement and formation of flux tubes in supersymmetric gauge theories [6,7,8,9,10,11,12,13,14,15,16]. One important particular feature of supersymmetric theories is the presence of modular spaces -manifolds on which scalar fields can develop arbitrary VEV's.…”

BPS Alice strings

“…The effect of a flat direction on BPS vortices of the ANO type was discussed in refs. [41,42]. Now we show that the BPS equations can be obtained by imposing SUSY transformation of the fermions to be zero.…”