Gluing affine vortices

TL;DR

This paper develops a gluing map for affine vortices with boundary conditions, facilitating the connection between gauged linear and nonlinear sigma models involving Lagrangian branes.

Contribution

It introduces a novel gluing construction for affine vortices with boundary conditions, crucial for linking different sigma models in symplectic geometry.

Findings

Constructed a gluing map for affine vortices with boundary conditions.

Established the role of this construction in relating gauged linear and nonlinear sigma models.

Provided a framework for understanding Lagrangian branes in the context of affine vortices.

Abstract

We construct a gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition at a rigid, regular, codimension one configuration. This construction plays an important role in establishing the relation between the gauged linear sigma model and the nonlinear sigma model in the presence of Lagrangian branes.