New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$

Izar Alonso

doi:10.1016/j.geomphys.2024.105292

New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$

Differential Geometry 2024-09-04 v2

Authors: Izar Alonso

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Abstract

We study the existence of $\text{SU}(2)^2$ -invariant $G_2$ -instantons on $\mathbb{R}^4 \times S^3$ with the coclosed $G_2$ -structures found on [arXiv:2209.02761]. We find an explicit 1-parameter family of $\text{SU}(2)^3$ -invariant $G_2$ -instantons on the trivial bundle on $\mathbb{R}^4 \times S^3$ and study its ''bubbling'' behaviour. We prove the existence a 1-parameter family on the identity bundle. We also provide existence results for locally defined $\text{SU}(2)^2$ -invariant $G_2$ -instantons.

Keywords

G_2-instantons coclosed G_2-structures R^4 x S^3 SU(2)-invariance bubbling behaviour

Cite

@article{arxiv.2311.08378,
  title  = {New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$},
  author = {Izar Alonso},
  journal= {arXiv preprint arXiv:2311.08378},
  year   = {2024}
}

Comments

24 pages, 1 figure, v2: minor changes. Accepted version for Journal of Geometry and Physics

New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$

Abstract

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