Coupled $\operatorname{G}_2$-instantons
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929336755421184 |
|---|---|
| author | Silva Jr., Agnaldo A. da Garcia-Fernandez, Mario Lotay, Jason D. Earp, Henrique N. Sá |
| author_facet | Silva Jr., Agnaldo A. da Garcia-Fernandez, Mario Lotay, Jason D. Earp, Henrique N. Sá |
| contents | We introduce the coupled instanton equations for a metric, a spinor, a three-form, and a connection on a bundle, over a spin manifold. Special solutions in dimensions $6$ and $7$ arise, respectively, from the Hull--Strominger and the heterotic $\operatorname{G}_2$ system. The equations are motivated by recent developments in theoretical physics and can be recast using generalized geometry; we investigate how coupled instantons relate to generalized Ricci-flat metrics and also to Killing spinors on a Courant algebroid. We present two open questions regarding how these different geometric conditions are intertwined, for which a positive answer is expected from recent developments in the physics literature by De la Ossa, Larfors and Svanes, and in the mathematics literature on Calabi--Yau manifolds, in recent work by the second-named author with González Molina. We give a complete solution to the first of these problems, providing a new method for the construction of instantons in arbitrary dimensions. For $\operatorname{G}_2$-structures with torsion coupled to $\operatorname{G}_2$-instantons, in dimension $7$, we also establish results around the second problem. The last part of the present work carefully studies the approximate solutions to the heterotic $\operatorname{G}_2$-system constructed by the third and fourth authors on contact Calabi--Yau $7$-manifolds, for which we prove the existence of approximate coupled $\operatorname{G}_2$-instantons and generalized Ricci-flat metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12937 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coupled $\operatorname{G}_2$-instantons Silva Jr., Agnaldo A. da Garcia-Fernandez, Mario Lotay, Jason D. Earp, Henrique N. Sá Differential Geometry High Energy Physics - Theory We introduce the coupled instanton equations for a metric, a spinor, a three-form, and a connection on a bundle, over a spin manifold. Special solutions in dimensions $6$ and $7$ arise, respectively, from the Hull--Strominger and the heterotic $\operatorname{G}_2$ system. The equations are motivated by recent developments in theoretical physics and can be recast using generalized geometry; we investigate how coupled instantons relate to generalized Ricci-flat metrics and also to Killing spinors on a Courant algebroid. We present two open questions regarding how these different geometric conditions are intertwined, for which a positive answer is expected from recent developments in the physics literature by De la Ossa, Larfors and Svanes, and in the mathematics literature on Calabi--Yau manifolds, in recent work by the second-named author with González Molina. We give a complete solution to the first of these problems, providing a new method for the construction of instantons in arbitrary dimensions. For $\operatorname{G}_2$-structures with torsion coupled to $\operatorname{G}_2$-instantons, in dimension $7$, we also establish results around the second problem. The last part of the present work carefully studies the approximate solutions to the heterotic $\operatorname{G}_2$-system constructed by the third and fourth authors on contact Calabi--Yau $7$-manifolds, for which we prove the existence of approximate coupled $\operatorname{G}_2$-instantons and generalized Ricci-flat metrics. |
| title | Coupled $\operatorname{G}_2$-instantons |
| topic | Differential Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.12937 |