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

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  • Ahmad Reza Haj Saeedi Sadegh
  • Minh Lam Nguyen

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 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.

Suggested Citation

  • Ahmad Reza Haj Saeedi Sadegh & Minh Lam Nguyen, 2025. "The three‐dimensional Seiberg–Witten equations for 3/2$3/2$‐spinors: A compactness theorem," Mathematische Nachrichten, Wiley Blackwell, vol. 298(10), pages 3331-3375, October.
  • Handle: RePEc:bla:mathna:v:298:y:2025:i:10:p:3331-3375
    DOI: 10.1002/mana.70042
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