  It has been known for a long time that vacuum polarization in QED leads to a
superluminal low-frequency phase velocity for light propagating in curved
spacetime. Assuming the validity of the Kramers-Kronig dispersion relation,
this would imply a superluminal wavefront velocity and the violation of
causality. Here, we calculate for the first time the full frequency dependence
of the refractive index using world-line sigma model techniques together with
the Penrose plane wave limit of spacetime in the neighbourhood of a null
geodesic. We find that the high-frequency limit of the phase velocity (i.e. the
wavefront velocity) is always equal to c and causality is assured. However, the
Kramers-Kronig dispersion relation is violated due to a non-analyticity of the
refractive index in the upper-half complex plane, whose origin may be traced to
the generic focusing property of null geodesic congruences and the existence of
conjugate points. This puts into question the issue of micro-causality, i.e.
the vanishing of commutators of field operators at spacelike separated points,
in local quantum field theory in curved spacetime.
