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TThe problem of fermion masses hierarchy in the Standard Model is consideredon a toy model of a 10-dimensional space-time with a IIA supergravity typebackground. Dirac equation on this background, after compactification of extra4- and 1-dimensional subspaces, gives the spectrum of Fermi fields whichprofiles in 5 dimensions and corresponding Higgs generated masses in 4dimensions depend on the eigenvalues of Dirac operator on the named compactsubspaces. Schwarzschild Euclidean deformation of the supergravity throat withthe "apple-shaped" conical singularity permits to leave only threenon-divergent angular modes interpreted as three generations of the down-typequarks. Calculated ratio $m_{d} / m_{s} = e^{-3}$ exactly coincides with itsexperimentally observed value for integer values of two free parameters of the10-dimensional background. Equations for non-chiral modes coincide with thenon-relativistic Schr\"odinger equation for an electron moving in a Coulombfield; the corresponding small fermion masses generated by the twisted boundaryconditions are expressed through the degenerate hypergeometric functions.

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