Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

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.

24 pages. This is a revised version, with some typos corrected. To appear in Commun. Math. Phys

References in corpus (5)

• Liouville Theorems for Dirac-Harmonic Maps
• Some aspects of Dirac-harmonic maps with curvature term
• Super Riemann surfaces, metrics, and gravitinos
• Energy estimates for the supersymmetric nonlinear sigma model and applications
• Symmetries and conservation laws of a nonlinear sigma model with gravitino

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• Energy quantization for a nonlinear sigma model with critical gravitinos
• Geometric analysis of the Yang-Mills-Higgs-Dirac model
• Some analytic results on interpolating sesqui-harmonic maps
• Coarse Regularity of Solutions to a Nonlinear Sigma-model with~$L^p$~gravitino
• From harmonic maps to the nonlinear supersymmetric sigma model of quantum field theory. At the interface of theoretical physics, Riemannian geometry and nonlinear analysis
• Dirac-harmonic maps with potential
• J-holomorphic curves and Dirac-harmonic maps
• The Super-Toda System and Bubbling of Spinors