The gauge symmetry of the Standard Model is SU(3)_c x SU(2)_L x U(1)_Y for
unknown reasons. One aspect that can be addressed is the low dimensionality of
all its subgroups. Why not much larger groups like SU(7), or for that matter,
SP(38) or E7? We observe that fermions charged under large groups acquire much
bigger dynamical masses, all things being equal at a high e.g. GUT scale, than
ordinary quarks. Should such multicharged fermions exist, they are too heavy to
be observed today and have either decayed early on (if they couple to the rest
of the Standard Model) or become reliquial dark matter (if they don't). The
result follows from strong antiscreening of the running coupling for those
larger groups (with an appropriately small number of flavors) together with
scaling properties of the Dyson-Schwinger equation for the fermion mass.Comment: 15 pages, 17 plots. This version incorporates community as well as
referee comments. Accepted for publication in Nuclear Physics
