# Gauged vortices in a background

@article{Romo2005GaugedVI, title={Gauged vortices in a background}, author={N. M. Rom{\~a}o}, journal={Journal of Physics A}, year={2005}, volume={38}, pages={9127-9144} }

We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class of the Abelian Higgs model approximately truncates to a finite-dimensional moduli space with a Kahler structure. For the case where the vortices live on a 2-sphere, we explain how localization formulae on the moduli spaces can be used to compute exactly the…

## 13 Citations

### Vortex counting and the quantum Hall effect

- PhysicsJournal of High Energy Physics
- 2022

Abstract
We provide evidence for conjectural dualities between nonrelativistic Chern-Simons-matter theories and theories of (fractional, nonAbelian) quantum Hall fluids in 2 + 1 dimensions. At low…

### Dynamics of Abelian Vortices Without Common Zeros in the Adiabatic Limit

- Mathematics
- 2014

On a smooth line bundle L over a compact Kähler Riemann surface Σ, we study the family of vortex equations with a parameter s. For each $${s \in [1,\infty]}$$s∈[1,∞] , we invoke techniques in Bradlow…

### Volume of Moduli Space of Vortex Equations and Localization

- Mathematics
- 2011

We evaluate volume of moduli space of BPS vortices on a compact genus h Riemann surface Σh by using topological field theory and localization technique developed by Moore, Nekrasov and Shatashvili.…

### On the curvature of vortex moduli spaces

- Mathematics
- 2014

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of…

### Zeitschrift On the curvature of vortex moduli spaces

- Mathematics
- 2014

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of…

### Dynamics of Abelian Vortices Without Common Zeros in the Adiabatic Limit

- MathematicsCommunications in Mathematical Physics
- 2014

On a smooth line bundle L over a compact Kähler Riemann surface Σ, we study the family of vortex equations with a parameter s. For each s∈[1,∞]\documentclass[12pt]{minimal} \usepackage{amsmath}…

### On the curvature of vortex moduli spaces

- MathematicsMathematische Zeitschrift
- 2014

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of…

### The $L^2$ Volume of the Space of Holomorphic Maps from K\"ahler Riemann Surfaces to $\mathbb{CP}^k$

- Mathematics
- 2015

We prove the conjectural formula for the $L^2$ volume of the space of degree $r$ holomorphic maps from a compact K\"ahler Riemann surface of genus $b$ to $\pk$. This formula was posed in \cite{Ba}…

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