G2-instantons on the ALC members of the B7 family

Jakob Stein; Matt Turner

doi:10.1007/s10455-025-10003-6

G₂-instantons on the ALC members of the B7 family

Jakob Stein
, Matt Turner

Department of Mathematical Sciences

Universidade Estadual de Campinas

Research output: Contribution to journal › Article › peer-review

Abstract

Using co-homogeneity one symmetries, we construct a two-parameter family of non-abelian G2-instantons on every member of the asymptotically locally conical B7-family of G2-metrics on S3×R4, and classify the resulting solutions. These solutions can be described as perturbations of a one-parameter family of abelian instantons, arising from the Killing vector-field generating the asymptotic circle fibre. Generically, these perturbations decay exponentially to the model, but we find a one-parameter family of instantons with polynomial decay. Moreover, we relate the two-parameter family to a lift of an explicit two-parameter family of anti-self-dual instantons on Taub-NUT R4, fibred over S3 in an adiabatic limit.

Original language	English
Article number	22
Journal	Annals of Global Analysis and Geometry
Volume	67
Issue number	4
Early online date	23 May 2025
DOIs	https://doi.org/10.1007/s10455-025-10003-6
Publication status	Published - 30 Jun 2025

Data Availability Statement

No datasets were generated or analysed during the current study.

Acknowledgements

Special thanks to Lorenzo Foscolo, Jason Lotay, and Johannes Nordström for their helpful comments and discussions. The first author would also like to thank Derek Harland for drawing our attention to the reference [11], and to Henrique N. Sá Earp for his support of the project. Some of the formulae in §4.1 were obtained by the first author in relation to a separate joint project with Lorenzo Foscolo and Calum Ross.

Funding

The first author was funded by grant #2023/02809-3, São Paulo Research Foundation (FAPESP), under the BRIDGES Collaboration #2021/04065-6. The second author was funded by the EPSRC Studentship 2106787 and the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics #488631.

Funders	Funder number
Engineering and Physical Sciences Research Council	2106787

Keywords

Co-homogeneity one
G2-manifolds
Gauge theory
Instantons
Special holonomy

ASJC Scopus subject areas

Analysis
Geometry and Topology

Access to Document

10.1007/s10455-025-10003-6

https://arxiv.org/abs/2409.03886

Cite this

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AB - Using co-homogeneity one symmetries, we construct a two-parameter family of non-abelian G2-instantons on every member of the asymptotically locally conical B7-family of G2-metrics on S3×R4, and classify the resulting solutions. These solutions can be described as perturbations of a one-parameter family of abelian instantons, arising from the Killing vector-field generating the asymptotic circle fibre. Generically, these perturbations decay exponentially to the model, but we find a one-parameter family of instantons with polynomial decay. Moreover, we relate the two-parameter family to a lift of an explicit two-parameter family of anti-self-dual instantons on Taub-NUT R4, fibred over S3 in an adiabatic limit.

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