Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

Abstract

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.

25 pages, 2 figures

Cited by in corpus (10)

• Stability Walls in Heterotic Theories
• Geometric constraints in dual F-theory and heterotic string compactifications
• Machine Learned Calabi-Yau Metrics and Curvature
• Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
• Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
• Universes as Big Data
• Machine Learning on generalized Complete Intersection Calabi-Yau Manifolds
• Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory $B-L$ MSSM
• cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature
• Yukawa Textures From Singular Spectral Data