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arXiv · hep-th/0103173

Spin-3/2 Fermions in Twistor Formalism

Mitsuo J. Hayashi
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Abstract

Consistency conditions for the local existence of massless spin 3/2 fields has been explored that the field equations for massless helicity 3/2 are consistent iff the space-time is Ricci-flat and that in Minkowski space-time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity 3/2 fields, we derive in flat space-time that the charges of spin-3/2 fields defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space-time that the (anti-)self-duality of the space-time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space-time to that with torsion (Einstein-Cartan theory) and have investigated the consistency of existence of spin 3/2 fields in it. A simple solution is found that the space-time has to be conformally (anti-)self-dual, left-(or right-)torsion-free. The integrability condition on $α$-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed-torsion.

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Mitsuo J. Hayashi. 2001-12-11. Spin-3/2 Fermions in Twistor Formalism. https://doi.org/10.1142/s0217732301005412

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