Chiral spectrum of the universal tuned (SU(3) × SU(2) × U(1))/ℤ 6 4D F-theory model

We use the recently developed methods of arXiv:2108.07810 to analyze vertical flux backgrounds and associated chiral matter spectra in the 4D universal (SU(3) × SU(2) × U(1))/ℤ6 model introduced in arXiv:1912.10991, which is believed to describe the most generic family of F-theory vacua with tuned (SU(3) × SU(2) × U(1))/ℤ6 gauge symmetry. Our analysis focuses on a resolution of a particular presentation of the (SU(3) × SU(2) × U(1))/ℤ6 model in which the elliptic fiber is realized as a cubic in ℙ2 fibered over an arbitrary smooth threefold base. We show that vertical fluxes can produce nonzero multiplicities for all chiral matter families that satisfy 4D anomaly cancellation, which include as a special case the chiral matter families of the Minimal Supersymmetric Standard Model.