# Magnetic Field and Curvature Effects on Pair Production II: Vectors and Implications for Chromodynamics

## TL;DR

This paper investigates how magnetic fields and space curvature influence pair production rates of vector particles, revealing effects of Nielsen-Olesen instability and implications for confinement in nonabelian gauge theories.

## Contribution

It extends previous work by calculating pair production rates for vector particles on curved spaces with magnetic fields, analyzing instability effects and their relevance to nonabelian confinement.

## Key findings

- Curvature and magnetic fields significantly affect pair production rates.
- Nielsen-Olesen instability is characterized on curved spaces.
- Results suggest links between pair production and confinement mechanisms.

## Abstract

We calculate the pair production rates for spin-$1$ or vector particles on spaces of the form $M \times {\mathbb R}^{1,1}$ with $M$ corresponding to ${\mathbb R}^2$ (flat), $S^2$ (positive curvature) and $H^2$ (negative curvature), with and without a background (chromo)magnetic field on $M$. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for $S^2$ and $H^2$ is obtained. We also give a brief discussion of how our results relate to ideas about confinement in nonabelian theories.