Abstract
N=1 supergravities with SO(2 2 n+1 ) gauge groups are local chiral anomaly free at 1-loop in D=4 n+2 dimensions ( n≥0), as are SO(32) type I superstrings in 10 D. We show that at 2-loops only D=6 and D=10 theories remain anomaly free, so a generalized Adler-Bardeen theorem continues to hold in these cases when the Green-Schwarz mechanism is used to cancel subleading and mixed anomalies.
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