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MiS Preprint
68/2016
Regularity of Solutions of the Nonlinear Sigma Model with Gravitino
Jürgen Jost, Enno Keßler, Jürgen Tolksdorf, Ruijun Wu and Miaomiao Zhu
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.
