Dimension Reduction of Generalized ASD Instantons

Fuente: arXiv
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Hauptverfasser: Galt, Dylan, Ma, Langte
Format: Preprint
Veröffentlicht: 2024
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author Galt, Dylan
Ma, Langte
author_facet Galt, Dylan
Ma, Langte
contents We study generalized anti-self-dual instantons defined over Riemannian manifolds equipped with a parallel codimension-$4$ differential form. In particular, for product Riemannian manifolds possessing such a form, we study dimension reduction phenomena, finding a topological criterion for bundles which, when satisfied, allows for a complete characterization of dimension reduction for the corresponding moduli space of generalized ASD instantons. By establishing an integrability result for families of connections, we then deduce explicit descriptions for these moduli spaces, including those of Hermitian Yang--Mills connections, $G_2$-, and $\Spin(7)$-instantons. When one factor in the product is a $4$-manifold, we establish well-behaved compactifications for these moduli spaces.
format Preprint
id arxiv_https___arxiv_org_abs_2405_17086
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Dimension Reduction of Generalized ASD Instantons
Galt, Dylan
Ma, Langte
Differential Geometry
Mathematical Physics
We study generalized anti-self-dual instantons defined over Riemannian manifolds equipped with a parallel codimension-$4$ differential form. In particular, for product Riemannian manifolds possessing such a form, we study dimension reduction phenomena, finding a topological criterion for bundles which, when satisfied, allows for a complete characterization of dimension reduction for the corresponding moduli space of generalized ASD instantons. By establishing an integrability result for families of connections, we then deduce explicit descriptions for these moduli spaces, including those of Hermitian Yang--Mills connections, $G_2$-, and $\Spin(7)$-instantons. When one factor in the product is a $4$-manifold, we establish well-behaved compactifications for these moduli spaces.
title Dimension Reduction of Generalized ASD Instantons
topic Differential Geometry
Mathematical Physics
url https://arxiv.org/abs/2405.17086