Partial Regularity for a Nonlinear Sigma Model with Gravitino in Higher Dimensions
Jürgen Jost, Ruijun Wu, and Miaomiao Zhu
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Submission date: 13. Sep. 2017
published in: Calculus of variations and partial differential equations, 57 (2018) 3, art-no. 85
DOI number (of the published article): 10.1007/s00526-018-1366-2
MSC-Numbers: 53C27, 58J05, 35J50
Keywords and phrases: nonlinear sigma model, gravitino, partial regularity, stationary solution
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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.