First-principles determination of fermion mass values and hierarchies

Determine from first principles the values of the Standard Model quark and lepton masses and characterize their hierarchical structure, for example within string theory compactifications that reproduce the MSSM spectrum, by computing the physical Yukawa couplings and matter-field Kähler metrics to achieve quantitative agreement with observed fermion masses and hierarchies.

Background

The paper addresses the longstanding challenge of deriving Standard Model fermion masses directly from a fundamental theory. While string theory provides a framework where such calculations are, in principle, possible, practical obstacles have historically prevented full computations, notably the need for explicit Ricci-flat Calabi–Yau metrics, Hermitian Yang–Mills bundle metrics, and harmonic bundle-valued forms.

The authors develop and demonstrate a machine-learning-based methodology for numerically approximating these geometric quantities in a realistic heterotic line bundle model, enabling the computation of physical Yukawa couplings. Their results illustrate moduli dependence and the importance of matter-field normalization, moving toward resolving the broader open problem.