Witten effect, anomaly inflow, and charge teleportation

We study a phenomenon that electric charges are “teleported” between two spatially separated objects without exchanging charged particles at all. For example, this phenomenon happens between a magnetic monopole and an axion string in four dimensions, two vortices in three dimensions, and two M5-branes in M-theory in which M2-charges are teleported. This is realized by anomaly inflow into these objects in the presence of cubic Chern-Simons terms. In particular, the Witten effect on magnetic monopoles can be understood as a general consequence of anomaly inflow, which implies that some anomalous quantum mechanics must live on them. Charge violation occurs in the anomalous theories living on these objects, but it happens in such a way that the total charge is conserved between the two spatially separated objects. We derive a formula for the amount of the charge which is teleported between the two objects in terms of the linking number of their world volumes in spacetime.