A compactness theorem for the Seiberg-Witten equation with multiple spinors in dimension three

TL;DR

This paper establishes a compactness theorem for solutions to the Seiberg-Witten equations with multiple spinors in three dimensions, showing their degeneration behavior converges to Fueter sections of ASD instanton moduli spaces.

Contribution

It introduces a new compactness result for the Seiberg-Witten equations with multiple spinors, linking their degeneration to Fueter sections of ASD instanton moduli spaces.

Findings

Solutions degenerate only via rescaling to Fueter sections

Degeneration characterized by convergence to ASD instanton moduli spaces

Provides a rigorous framework for understanding solution limits

Abstract

We prove that a sequence of solutions of the Seiberg-Witten equation with multiple spinors in dimension three can degenerate only by converging (after rescaling) to a Fueter section of a bundle of moduli spaces of ASD instantons.