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arXiv · 2609.24551

Dirac-harmonic maps from manifolds with boundary via index theory

Volker Branding·Nicolas Ginoux
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Abstract

Dirac-harmonic maps are a mathematical version of the supersymmetric non-linear sigma model of quantum field theory. Since they arise as critical points of an unbounded energy functional, it is a challenging task to establish general existence results. Within this manuscript we mainly prove a general existence result based on index theory for manifolds with boundary and apply it in various situations. Due to the presence of a boundary there are additional contributions in the Atiyah-Patodi-Singer index formula allowing for a non-vanishing index, which is the key argument in our proofs. Further explicit examples based on twistor spinors on surfaces are also presented.

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Volker Branding, Nicolas Ginoux. 2026-09-21. Dirac-harmonic maps from manifolds with boundary via index theory. https://arxiv.org/abs/2609.24551

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