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Symmetries and conservation laws of a nonlinear sigma model with gravitino
Jürgen Jost, Enno Keßler, Jürgen Tolksdorf, Ruijun Wu and Miaomiao Zhu
We show that the action functional of the nonlinear sigma model with gravitino considered in a previous article  is invariant under rescaled conformal transformations, super Weyl transformations and diffeomorphisms. We give a careful geometric explanation how a variation of the metric leads to the corresponding variation of the spinors. In particular cases and despite using only commutative variables, the functional possesses a degenerate super symmetry. The corresponding conservation laws lead to a geometric interpretation of the energy-momentum tensor and supercurrent as holomorphic sections of appropriate bundles.