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The full 6d Hopf-Wess-Zumino term in the action functional for the M5-braneis anomalous as traditionally defined. What has been missing is a conditionimplying the higher analogue of level quantization familiar from the 2dWess-Zumino term. We prove that the anomaly cancellation condition is impliedby the hypothesis that the C-field is charge-quantized in twisted Cohomotopytheory. The proof follows by a twisted/parametrized generalization of the Hopfinvariant, after identifying the full 6d Hopf-Wess-Zumino term with a twistedhomotopy Whitehead integral formula, which we establish.

Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino term of the M5-brane