PreprintCC BY-NC-ND 4.0HAL
Dirac-harmonic maps from manifolds with boundary via index theory
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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BibTeX
@misc{branding2026diracharmonic,
title = {{Dirac-harmonic maps from manifolds with boundary via index theory}},
author = {Volker Branding and Nicolas Ginoux},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24551},
eprint = {2609.24551},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05757916v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Dirac-harmonic maps from manifolds with boundary via index theory
AU - Volker Branding
AU - Nicolas Ginoux
PY - 2026
DA - 2026/09/21
PB - HAL
DO - 10.48550/arxiv.2609.24551
UR - https://hal.science/hal-05757916v1
AB - 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.
ER -