Parallel torsion and $G_2, Spin(7)$ instantons

Fuente: arXiv
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Main Authors: Ivanov, Stefan, Petkov, Alexander, Ugarte, Luis
Format: Preprint
Published: 2025
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author Ivanov, Stefan
Petkov, Alexander
Ugarte, Luis
author_facet Ivanov, Stefan
Petkov, Alexander
Ugarte, Luis
contents Instanton properties of the characteristic connection $\nabla$ on an integrable $G_2$ manifold as well as instanton condition of the torsion connection $\nabla$ on a $Spin(7)$ manifold are investigated. It is shown that for an integrable $G_2$ manifold with $\nabla$-parallel Lee form the curvature of the characteristic connection is a $G_2$ instanton exactly when the torsion 3-form is $\nabla$-parallel. It is observed that on a compact $Spin(7)$ manifold with $\nabla$ closed torsion 3-form the torsion connection is a $Spin(7)$ instanton if and only if the torsion 3-form is parallel with respect to the torsion connection.
format Preprint
id arxiv_https___arxiv_org_abs_2509_10623
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Parallel torsion and $G_2, Spin(7)$ instantons
Ivanov, Stefan
Petkov, Alexander
Ugarte, Luis
Differential Geometry
High Energy Physics - Theory
Instanton properties of the characteristic connection $\nabla$ on an integrable $G_2$ manifold as well as instanton condition of the torsion connection $\nabla$ on a $Spin(7)$ manifold are investigated. It is shown that for an integrable $G_2$ manifold with $\nabla$-parallel Lee form the curvature of the characteristic connection is a $G_2$ instanton exactly when the torsion 3-form is $\nabla$-parallel. It is observed that on a compact $Spin(7)$ manifold with $\nabla$ closed torsion 3-form the torsion connection is a $Spin(7)$ instanton if and only if the torsion 3-form is parallel with respect to the torsion connection.
title Parallel torsion and $G_2, Spin(7)$ instantons
topic Differential Geometry
High Energy Physics - Theory
url https://arxiv.org/abs/2509.10623