2024/04/19 by Agnaldo A. da Silva, Silva, Agnaldo A. da, Mario García-Fernández +5
Computer Science · Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Matrix Theory and Algorithms #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2404.12937
openalex publication_date 2024/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 G2 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 G2-structures with torsion coupled to G2-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 G2-system constructed by the third and fourth authors on contact Calabi--Yau 7-manifolds, for which we prove the existence of approximate coupled G2-instantons and generalized Ricci-flat metrics.