The M5-brane anomaly

The problem of the M5-brane anomaly cancellation is addressed. We reformulate FHMM construction [D. Freed et al., Adv. Theor. Math. Phys. 2 (1998) 601] making explicit the relation with the M5-brane SUGRA solution. We suggest another solution to the magnetic coupling equation which does not need anomalous SO(5) variation of the 3-form potential and coincides with the SUGRA solution outside smoothed out core of the magnetic source. Chern–Simons term evaluated on this solution generates the same anomaly inflow as achieved by FHMM.