# Dual formulations of vortex strings in supersymmetric Abelian Higgs model

## TL;DR

This paper explores dual formulations of vortex strings in a supersymmetric Abelian Higgs model, revealing how vortex strings and their superpartners are represented in different superfield frameworks with explicit couplings.

## Contribution

It introduces two dual superfield formulations of vortex strings in a supersymmetric gauge theory, clarifying their descriptions and couplings in superspace and component form.

## Key findings

- Dual Lagrangians describe vortex strings via 2-form gauge fields.
- Vortex strings are embedded in superfields with explicit superpartner couplings.
- The formulations include both superspace and component descriptions.

## Abstract

We discuss dual formulations of vortex strings (magnetic flux tubes) in the four-dimensional ${\cal N} =1$ supersymmetric Abelian Higgs model with the Fayet--Iliopoulos term in the superspace formalism. The Lagrangian of the model is dualized into a Lagrangian of the $BF$-type described by a chiral spinor gauge superfield including a 2-form gauge field. The dual Lagrangian is further dualized into a Lagrangian given by a chiral spinor superfield including a massive 2-form field. In both of the dual formulations, we obtain a superfield into which the vortex strings and their superpartners are embedded. We show the dual Lagrangians in terms of a superspace and a component formalism. In these dual Lagrangians, we explicitly show that the vortex strings of the original model are described by a string current electrically coupled with the 2-form gauge field or the massive 2-form field.