The three-dimensional Seiberg-Witten equations for 3/2-spinors: a compactness theorem

Abstract

The Rarita-Schwinger-Seiberg-Witten (RS-SW) equations are defined similarly to the classical Seiberg-Witten equations, where a geometric non-Dirac-type operator replaces the Dirac operator called the Rarita-Schwinger operator. In dimension four, the RS-SW equation was first considered by the second-named author. The variational approach will also give us a three-dimensional version of the equations. The RS-SW equations share some features with the multiple-spinor Seiberg-Witten equations, where the moduli space of solutions could be non-compact. In this note, we prove a compactness theorem regarding the moduli space of solutions of the RS-SW equations defined on 3-manifolds.