The Berry connection of the Ginzburg-Landau vortices

TL;DR

This paper investigates the geometric properties of Ginzburg-Landau vortices, deriving asymptotic formulas for their moduli space tangent vectors and computing the Berry curvature and holonomy in large volume limits.

Contribution

It provides new asymptotic formulas for the tangent vectors of vortex moduli spaces and computes the Berry curvature and holonomy at critical coupling.

Findings

Asymptotic formulas for tangent vectors of vortex moduli space

Explicit computation of Berry curvature and holonomy in large volume limit

Insights into the geometric structure of Ginzburg-Landau vortices

Abstract

We analyze 2-dimensional Ginzburg-Landau vortices at critical coupling, and establish asymptotic formulas for the tangent vectors of the vortex moduli space using theorems of Taubes and Bradlow. We then compute the corresponding Berry curvature and holonomy in the large volume limit.