Dirac-harmonic maps from degenerating spin surfaces I: the Neveu-Schwarz case

TL;DR

This paper investigates Dirac-harmonic maps from degenerating spin surfaces with bounded energy, establishing a generalized energy identity and compactness conditions in the Neveu-Schwarz case.

Contribution

It introduces necessary and sufficient conditions for the compactness of Dirac-harmonic maps from degenerating spin surfaces with Neveu-Schwarz nodes.

Findings

Generalized energy identity established for degenerating spin surfaces.

Necessary and sufficient conditions for $W^{1,2} imes L^{4}$ modulo bubbles compactness.

Analysis focused on the Neveu-Schwarz type degenerations.

Abstract

We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We find condition that is both necessary and sufficient for the $W^{1,2} \times L^{4}$ modulo bubbles compactness of a sequence of such maps.