Hermitian Yang--Mills connections on general vector bundles: geometry and physical Yukawa couplings
This work addresses a computational challenge in string theory for physicists, providing a general method to compute Yukawa couplings, though it appears incremental as it builds on existing geometric machine learning approaches.
The authors tackled the problem of computing Hermitian Yang-Mills connections on holomorphic vector bundles by developing an alternating optimization method based on geometric machine learning, enabling the calculation of physically normalized Yukawa couplings in heterotic string compactifications, as demonstrated for a non-Abelian structure group.
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.