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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Partial Regularity for a Nonlinear Sigma Model with Gravitino in Higher Dimensions
Jürgen Jost, Ruijun Wu and Miaomiao ZhuAbstract
We study the regularity problem of the nonlinear sigma model with gravitino fields in higher dimensions. After setting up the geometric model, we derive the Euler--Lagrange equations and consider the regularity of weak solutions defined in suitable Sobolev spaces. We show that any weak solution is actually smooth under some smallness assumption for certain Morrey norms. By assuming some higher integrability of the vector spinor, we can show a partial regularity result for stationary solutions, provided the gravitino is critical, which means that the corresponding supercurrent vanishes. Moreover, in dimension less than 6, partial regularity holds for stationary solutions with respect to general gravitino fields.
- Received:
- 13.09.17
- Published:
- 14.09.17
- MSC Codes:
- 53C27, 58J05, 35J50
- Keywords:
- nonlinear sigma model, gravitino, partial regularity, stationary solution