  In the first part, the induced vacuum spin around an Aharonov-Bohm flux
string in massless three-dimensional QED is computed explicitly and the result
is shown to agree with a general index theorem. A previous observation in the
literature, that the presence of induced vacuum quantum numbers which are not
periodic in the flux make an integral-flux AB string visible, is reinforced. In
the second part, a recent discussion of chiral symmetry breaking by external
magnetic fields in parity invariant QED$_3$ and its relation to the induced
spin in parity non-invariant QED$_3$ is further elaborated. Finally other
vacuum polarisation effects around flux tubes in different variants of QED, in
three and four dimensions are mentioned.
