  We investigate charge quantization in the Standard Model (SM) through a
$\mathbb{CP}^2$ nonlinear sigma model (NLSM), $SU(3)_G/(SU(2)_H \times
U(1)_H)$, and a $\mathbb{CP}^3$ model, $SU(4)_G/(SU(3)_H \times U(1)_H)$. We
also generalize to any $\mathbb{CP}^k$ model. Charge quantization follows from
the consistency and dynamics of the NLSM, without a monopole or Grand Unified
Theory, as shown in our earlier work on the $\mathbb{CP}^1$ model
(arXiv:1309.0692). We find that representations of the matter fields under the
unbroken non-abelian subgroup dictate their charge quantization under the
$U(1)_H$ factor. In the $\mathbb{CP}^2$ model the unbroken group is identified
with the weak and hypercharge groups of the SM, and the Nambu-Goldstone boson
(NGB) has the quantum numbers of a SM Higgs. There is the intriguing
possibility of a connection with the vanishing of the Higgs self-coupling at
the Planck scale. Interestingly, with some minor assumptions (no vector-like
matter and minimal representations) and starting with a single quark doublet,
anomaly cancellation requires the matter structure of a generation in the SM.
Similar analysis holds in the $\mathbb{CP}^3$ model, with the unbroken group
identified with QCD and hypercharge, and the NGB having the up quark as a
partner in a supersymmetric model. This can motivate solving the strong CP
problem with a vanishing up quark mass.
