Hermitian Yang-Mills connections on general vector bundles: geometry and physical Yukawa couplings

We compute solutions to the Hermitian Yang-Mills equations on holomorphic vector bundles V via an alternating optimisation procedure founded on geometric machine learning. The proposed method is fully general with respect to the rank and structure group of V, requiring only the ability to enumerate a basis of global sections for a given bundle. This enables us to compute the physically normalised Yukawa couplings in a broad class of heterotic string compactifications. Using this method, we carry out this computation in full for a heterotic compactification incorporating a gauge bundle with non-Abelian structure group.