String theory provides us with 8d supersymmetric gauge theory with gauge algebras su(N),so(2N),sp(N),e6,e7ande8, but no construction for so(2 N+ 1) , f4 and g2 is known. In this paper, we show that the theories for f4 and so(2 N+ 1) have a global gauge anomaly associated to πd=8, while g2 does not have it. We argue that the anomaly associated to πd in d-dimensional gauge theories cannot be canceled by topological degrees of freedom in general. We also show that the theories for sp(N) have a subtler gauge anomaly, which we suggest should be canceled by a topological analogue of the Green-Schwarz mechanism.
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