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We define a variant of the Seiberg-Witten equations using theRarita-Schwinger operators for closed simply connected spin smooth 4-manifoldX. The moduli space of solutions to the system of non-linear differentialequations consist of harmonic 3/2-spinors and connections satisfying certaincurvature condition. Beside having an obvious U(1)-symmetry, these equationsalso have a symmetry by Pin(2). We exploit this additional symmetry to performfinite dimensional approximations for the eigenvalue problem of the3/2-monopole map and show that under a certain topological assumption, themoduli space of solutions is always non-compact, and thus non-empty.

Pin(2)-equivariance of the Rarita-Schwinger-Seiberg-Witten Equations