The three-dimensional Seiberg–Witten equations for 3 / 2 $3/2$ -spinors: A compactness theorem

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 4, the RS–SW equation was first considered by the second author (Nguyen [J. Geom. Anal. 33(2023), no. 10, 336]). 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 noncompact. In this paper, we prove a compactness theorem regarding the moduli space of solutions of the RS–SW equations defined on 3-manifolds.