Duality of topological superconductors begets Josephson currents induced by the Witten effect

We consider the field theory of a superconductor with a topological axion term and construct its dual theories for both bulk and boundary at strong coupling. The theory describes, e.g., a conventional superconductor sandwiched between two topological insulators. The interacting topological states that emerge are classified by a \(\mathbb{Z}_8\) invariant and the strong coupling boundary theory is shown to be purely topological. These topological states lack a non-interacting equivalent. Due to the Witten effect, magnetic monopoles attain a fractional electric charge. This leads to an anomalous AC Josephson current generated by external magnetic fields.