Abstract
We show that theories with the Green-Schwarz mechanism of canceling local anomalies in even dimensions have the possibility of the worst type of global Yang-Mills chiral anomalies given by the homotopy group of the Yang-Mills gauge group. The examples are given for SU(3) gauge theories in six dimensions ({Pi}{sub 6}(SU(3))={ital Z}{sub 3 }) whose global anomalies are of types {bold Z}{sub 1}, {bold Z}{sub 2}, {bold Z}{sub 3}, and {bold Z}{sub 6}.
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