M5 bordism classifies the invertible phases of 6d (2,0) anomaly theories, and the Hopf-Wess-Zumino term is the phase that transgresses to the second Pontryagin class.
The global anomaly of the self-dual field in general backgrounds
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abstract
We prove a formula for the global gravitational anomaly of the self-dual field theory in the presence of background gauge fields, assuming the results of arXiv:1110.4639. Along the way, we also clarify various points about the self-dual field theory. In particular, we give a general definition of the theta characteristic entering its partition function and settle the issue of its possible metric dependence. We treat the cohomological version of type IIB supergravity as an example of the formalism: a mixed gauge-gravitational global anomaly, occurring when the B-field and Ramond-Ramond 2-form gauge fields have non-trivial Wilson lines, cancels provided a certain cobordism group vanishes.
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Anomaly Matching in 6d $\mathcal{N}=(2,0)$ SCFTs from M5 Cobordism
M5 bordism classifies the invertible phases of 6d (2,0) anomaly theories, and the Hopf-Wess-Zumino term is the phase that transgresses to the second Pontryagin class.