Abstract
Chiral color for strong interactions requires that the gauge group of elementary-particle interactions be at least $\mathrm{SU}{(3)}_{L}\mathrm{SU}{(3)}_{R}\mathrm{SU}{(2)}_{L}\mathrm{U}{(1)}_{Y}$. Under this symmetry the conventional quarks have triangle anomalies associated with chiral-color and weak hypercharge gauge interactions. These anomalies are canceled by adding exotic-quark representations of the group $\mathrm{SU}{(3)}_{L}\mathrm{SU}{(3)}_{R}\mathrm{SU}{(2)}_{L}\mathrm{U}{(1)}_{Y}$. Models with three generations of conventional quarks and leptons are presented as solutions to the constraints of anomaly cancellation.
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