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.
Geometry of 6D RG Flows
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abstract
We study renormalization group flows between six-dimensional superconformal field theories (SCFTs) using their geometric realizations as singular limits of F-theory compactified on elliptically fibered Calabi-Yau threefolds. There are two general types of flows: One corresponds to giving expectation values to scalars in the tensor multiplets (tensor branch flow) realized as resolving the base of the geometry. The other corresponds to giving expectation values to hypermultiplets (Higgs branch flow) realized as complex structure deformations of the geometry. To corroborate this physical picture we calculate the change in the anomaly polynomial for these theories, finding strong evidence for a flow from a UV fixed point to an IR fixed point. Moreover, we find evidence against non-trivial dualities for 6D SCFTs. In addition we find non-trivial RG flows for theories realizing small E8 instantons on ALE spaces.
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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.