C. Mishra

J. Tan

Canonical connections in string compactifications are computed for a broad class of bundles over Calabi-Yau manifolds by a new method.

Geometric compactifications in string theory enable low-energy physics to be derived from geometrical data describing certain highly curved spaces. We develop a new AI-based approach to computing Hermitian Yang–Mills connections on bundles over Calabi-Yau manifolds and conduct a first-principles derivation of key physical observables, opening an avenue to understanding the physics induced by different geometries.

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.

Physics of bundles

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