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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
77/2015

Geometric analysis of the action functional of the nonlinear supersymmetric sigma model

Jürgen Jost, Lei Liu and Miaomiao Zhu

Abstract

The mathematical version of the action functional of the nonlinear supersymmetric model of quantum field theory couples a map from a Riemann surface into a Riemannian manifold with a spinor field along the map. While a simplified version of the model, the so-called Dirac-harmonic map functional, has been extensively studied in the literature in recent years, the full model involves an additional curvature term. Handling the finer analytic aspects caused by this term requires new methods. These are developed in this paper. We analyze the blow-up of solutions. In particular, we show that the energy identities and no neck property hold during the blow-up process. In technical terms, we derive a new exponential decay estimate of some weighted energy on neck domains for the spinor field. This is based on some Hardy type inequality.

Received:
10.11.15
Published:
10.11.15

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Preprint
2015 Repository Open Access
Jürgen Jost, Lei Liu and Miaomiao Zhu

Geometric analysis of the action functional of the nonlinear supersymmetric sigma model