# Supersymmetric vortex defects in two dimensions

## TL;DR

This paper classifies and analyzes supersymmetric vortex defects in 2d N=(2,2) gauge theories, deriving correlators, exploring dualities, and establishing equivalences with coupled systems, advancing understanding of defect structures and mirror symmetry.

## Contribution

It provides a classification of vortex defect boundary conditions, a formula for defect correlators, and proves an equivalence with 0d-2d coupled systems in 2d supersymmetric theories.

## Key findings

- Derived a formula for defect correlators on the squashed sphere.
- Established an equivalence between vortex defects and 0d-2d coupled systems.
- Confirmed consistency of defect correlators with mirror symmetry dualities.

## Abstract

We study codimension-two BPS defects in 2d N=(2,2) supersymmetric gauge theories, focusing especially on those characterized by vortex-like singularities in the dynamical or non-dynamical gauge field. We classify possible SUSY-preserving boundary conditions on charged matter fields around the vortex defects, and derive a formula for defect correlators on the squashed sphere. We also prove an equivalence relation between vortex defects and 0d-2d coupled systems. Our defect correlators are shown to be consistent with the mirror symmetry duality between Abelian gauged linear sigma models and Landau-Ginzburg models, as well as that between the minimal model and its orbifold. We also study the vortex defects inserted at conical singularities.