Electric charge is quantized: all observed charges are integer multiples of e/3. The Standard Modelaccommodates this fact but does not explain it. The two existing explanations — Dirac's magneticmonopole argument (1931) and grand unification — both require physics beyond the StandardModel that has not been observed. We present a third mechanism: the Gaussian unit groupZi* = 1, i, -1, -i acts as a Z₄ symmetry on the 56-dimensional charge lattice of E₇ (7), theU-duality group of maximal supergravity in four dimensions. This Z₄ action forces the quarticinvariant I₄ — which determines black hole entropy — to be the lowest nontrivial polynomialinvariant, and restricts all charges to a discrete lattice. The mechanism requires no magneticmonopoles and no grand unification: it derives charge quantization from the arithmetic of Gaussianintegers acting on an exceptional Lie algebra's charge representation. We verify the Z₄ actionexplicitly on the full 56-dimensional representation and show that three independently defined Z₄symmetries (topological, algebraic, and Hamiltonian) act identically.
Robert A. Kenney (Sat,) studied this question.