Transmogrifying Fuzzy Vortices

TL;DR

This paper extends the construction of vortex solitons to a fuzzy linear sigma model with rich BPS solutions, connecting noncommutative vortices to string theory D-brane configurations.

Contribution

It provides an explicit construction of semilocal vortex solutions in a noncommutative setting and relates them to D-brane configurations in string theory.

Findings

Explicit degree-k semilocal vortex solutions constructed.

Infinite coupling limit relates vortices to noncommutative lumps.

Interpretation of sigma model solitons as D-strings between branes.

Abstract

We show that the construction of vortex solitons of the noncommutative Abelian-Higgs model can be extended to a critically coupled gauged linear sigma model with Fayet-Illiopolous D-terms. Like its commutative counterpart, this fuzzy linear sigma model has a rich spectrum of BPS solutions. We offer an explicit construction of the degree$-k$ static semilocal vortex and study in some detail the infinite coupling limit in which it descends to a degree$-k$ $\C\Pk^{N}$ instanton. This relation between the fuzzy vortex and noncommutative lump is used to suggest an interpretation of the noncommutative sigma model soliton as tilted D-strings stretched between an NS5-brane and a stack of D3-branes in type IIB superstring theory.