Geometric analysis of the action functional of the nonlinear supersymmetric sigma model
Jürgen Jost, Lei Liu, and Miaomiao Zhu
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Submission date: 10. Nov. 2015 (revised version: March 2017)
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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.