Energy quantization for a nonlinear sigma model with critical gravitinos
Jürgen Jost, Ruijun Wu, and Miaomiao Zhu
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Submission date: 12. Feb. 2017
MSC-Numbers: 35B44, 58J90, 58E20
Keywords and phrases: nonlinear sigma-model, supercurrent, energy identity, Pohozaev identity, gravitino, Dirac-harmonic map
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We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from supersymmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless and divergence-free energy-momentum tensor, which gives rise to a holomorphic quadratic differential. Using it we obtain a Pohozaev type identity and finally we can establish the energy identities along a weakly convergent sequence of fields with uniformly bounded energies.