Regularity of Solutions of the Nonlinear Sigma Model with Gravitino
Jürgen Jost, Enno Keßler, Jürgen Tolksdorf, Ruijun Wu, and Miaomiao Zhu
Contact the author: Please use for correspondence this email.
Submission date: 07. Oct. 2016
published in: Communications in mathematical physics, 358 (2018) 1, p. 171-197
DOI number (of the published article): 10.1007/s00220-017-3001-z
MSC-Numbers: 53C43, 35B65
Keywords and phrases: nonlinear sigma-model, Rivière regularity, gravitino
Download full preprint: PDF (566 kB)
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.