Examples of deformed G<sub>2</sub>-instantons/Donaldson–Thomas connections

Lotay, Jason D.; Oliveira, Gonçalo

doi:10.5802/aif.3465

Examples of deformed G₂-instantons/Donaldson–Thomas connections
[Exemples de G₂-instantons/connexions de Donaldson–Thomas déformées]

Lotay, Jason D.¹ ; Oliveira, Gonçalo ²

¹ University of Oxford, U.K.
² Universidade Federal Fluminense IME-GMA Niterói, Brazil

Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 339-366.

Résumé
Abstract

Dans cette note, nous fournissons les premiers exemples non triviaux de $G_{2}$ -instantons déformés, initialement appelés connexions Donaldson–Thomas déformées. En conséquence, on peut utiliser $G_{2}$ -instantons déformés pour faire la distinction entre des $G_{2}$ -structures presque parallèles et des $G_{2}$ -structures isométriques sur des 7-variétés 3-Sasakiennes. Nos exemples donnent des $G_{2}$ -instantons déformés non triviaux avec une théorie de la déformation obstruée et des situations où l’espace des modules des $G_{2}$ -instantons déformés a des composantes de dimensions différentes. Nous étudions enfin la relation entre nos exemples et une fonctionnelle de type Chern–Simons qui a les $G_{2}$ -instantons déformés en points critiques.

In this note, we provide the first non-trivial examples of deformed $G_{2}$ -instantons, originally called deformed Donaldson–Thomas connections. As a consequence, we see how deformed $G_{2}$ -instantons can be used to distinguish between nearly parallel $G_{2}$ -structures and isometric $G_{2}$ -structures on 3-Sasakian 7-manifolds. Our examples give non-trivial deformed $G_{2}$ -instantons with obstructed deformation theory and situations where the moduli space of deformed $G_{2}$ -instantons has components of different dimensions. We finally study the relation between our examples and a Chern–Simons type functional which has deformed $G_{2}$ -instantons as critical points.

Reçu le : 2020-08-04
Révisé le : 2020-12-31
Accepté le : 2021-01-27
Publié le : 2022-07-01

DOI : 10.5802/aif.3465

Classification : 53C07, 53C25
Keywords: Deformed $\mathrm{G}_2$-instantons, deformed Donaldson–Thomas connections, nearly parallel $\mathrm{G}_2$-structures, isometric $\mathrm{G}_2$-structures, 3-Sasakian.
Mot clés : $\mathrm{G}_2$-instantons déformés, connexions Donaldson–Thomas déformés, $\mathrm{G}_2$-structures presque parallèles, $\mathrm{G}_2$-structures isométriques, 3-Sasakien.

Affiliations des auteurs :

Lotay, Jason D. ¹ ; Oliveira, Gonçalo ²

¹ University of Oxford, U.K.
² Universidade Federal Fluminense IME-GMA Niterói, Brazil

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Examples of deformed {G\protect\textsubscript{2}-instantons/Donaldson{\textendash}Thomas} connections},
     journal = {Annales de l'Institut Fourier},
     pages = {339--366},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     year = {2022},
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Lotay, Jason D.; Oliveira, Gonçalo. Examples of deformed G₂-instantons/Donaldson–Thomas connections. Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 339-366. doi : 10.5802/aif.3465. https://aif.centre-mersenne.org/articles/10.5802/aif.3465/

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