Schwarzschild deformed supergravity background: Possible geometry origin of fermion generations and mass hierarchy

Abstract

The problem of fermion masses hierarchy in the Standard Model is considered on a toy model of a 10-dimensional space-time with a IIA supergravity type background. The Dirac equation written on this background, after compactification of extra four- and one-dimensional subspaces, gives the spectrum of Fermi fields which profiles in five dimensions and corresponding Higgs generated masses in four dimensions depend on the eigenvalues of Dirac operator on the named compact subspaces. Schwarzschild Euclidean deformation of the supergravity throat with the “apple-shaped” conical singularity permits to leave only three nondivergent angular modes interpreted as three generations of the down-type quarks. The resulting expressions for the quark masses are a geometry version of the Froggatt-Nielsen mechanism. Published by the American Physical Society 2024