Symmetries and conservation laws of a nonlinear sigma model with gravitino
Jürgen Jost, Enno Keßler, Jürgen Tolksdorf, Ruijun Wu, and Miaomiao Zhu
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Submission date: 21. Mar. 2017
MSC-Numbers: 37K05, 70S10, 58E30, 58E20
Keywords and phrases: nonlinear sigma model, gravitino, Noether's theorem, energy-momentum tensor, supercurrent, Dirac-harmonic map
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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.