Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

Abstract

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.

Coarse regularity of solutions to a nonlinear sigma-model with $$L^p$$ L p gravitino

“…In a recent work [19], a corresponding geometric model was set up and some analytical issues were studied. In contrast with the previous models which use anticommuting fields and which are therefore not directly amenable to the methods of geometric analysis, this model uses only commuting fields and thus is given within the context of Riemannian geometry.…”

“…Though this approach makes the supersymmetries involved less transparent, it has the advantages that this model is closely related to mathematically long-studied models such as harmonic maps and Dirac-harmonic maps and their various variants. In [19], a detailed setup for this two-dimensional nonlinear sigma model was developed. On this basis, now the regularity issues can be investigated.…”

“…On this basis, now the regularity issues can be investigated. The smoothness of weak solutions of the Euler-Lagrange equations, with smooth Riemannian metric and gravitino, was obtained in [19].…”

“…Let us briefly recall the framework of the model in [19]. For details we refer to that article and the references therein.…”

“…For a detailed clarification of these formulae we refer to [19]. For the cases of the simpler models, namely Dirac-harmonic maps and Dirac-harmonic maps with curvature terms, see [3,9,18,25,28].…”