# Abelian Higgs Vortices and Discrete Conformal Maps

## TL;DR

This paper links abelian Higgs vortices with discrete conformal maps, showing how discrete conformal theory can be used to construct vortex solutions through conformal mapping problems involving curvature and volume forms.

## Contribution

It establishes a novel connection between vortex solutions in Higgs models and discrete conformal maps, providing a new method for constructing vortex solutions.

## Key findings

- Discrete conformal maps can be used to construct vortex solutions.
- A new relationship between vortex theory and conformal mapping problems.
- The approach bridges continuous vortex models with discrete geometric structures.

## Abstract

We establish a connection between recent developments in the study of vortices in the abelian Higgs models, and in the theory of structure-preserving discrete conformal maps. We explain how both are related via conformal mapping problems involving prescribed linear combinations of the curvature and volume form, and show how the discrete conformal theory can be used to construct discrete vortex solutions.