Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

Jürgen Jost, Enno Keßler, Jürgen Tolksdorf, Ruijun Wu, and Miaomiao Zhu

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Submission date: 07. Oct. 2016
Pages: 26
published in: Communications in mathematical physics, 358 (2018) 1, p. 171-197 
DOI number (of the published article): 10.1007/s00220-017-3001-z
Bibtex
MSC-Numbers: 53C43, 35B65
Keywords and phrases: nonlinear sigma-model, Rivière regularity, gravitino
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Abstract:
We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler--Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière's regularity theory and Riesz potential theory.