2001/10/31 by Gabor Etesi, Gábor Etesi
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holonomy #Instanton #Mathematical physics #Mathematics #Physics #Pure mathematics #Spin (aerodynamics) #Spinor #gr-qc #hep-th
paper · pdf · doi:10.1016/s0370-2693(01)01239-4
published as Phys.Lett. B521 (2001) 391-399 · 10 pages, no figures, LaTeX. More references have been added; but this version differs from the published one
openalex publication_date 2001/11/01 · arxiv created 2001/11/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this Letter we establish a relationship between symmetric SU(2) Yang–Mills instantons and metrics with Spin(7) holonomy. Our method is based on a slight extension of that of Bryant and Salamon developed to construct explicit manifolds with special holonomies in 1989. More precisely, we prove that making use of symmetric SU(2) Yang–Mills instantons on Riemannian spin-manifolds, we can construct metrics on the chiral spinor bundle whose holonomy is within Spin(7). Moreover, if the resulting space is connected, simply connected and complete, the holonomy coincides with Spin(7). The basic explicit example is the metric constructed on the chiral spinor bundle of the round four-sphere by using a generic SU(2)-instanton of unit action; hence it is a five-parameter deformation of the Bryant–Salamon example, also found by Gibbons, Page and Pope.