  Cosmic shear surveys have great promise as tools for precision cosmology, but
can be subject to systematic errors including intrinsic ellipticity
correlations of the source galaxies. The intrinsic alignments are believed to
be small for deep surveys, but this is based on intrinsic and lensing
distortions being uncorrelated. Here we show that the gravitational lensing
shear and intrinsic shear need not be independent: correlations between the
tidal field and the intrinsic shear cause the intrinsic shear of nearby
galaxies to be correlated with the gravitational shear acting on more distant
galaxies. We estimate the magnitude of this effect for two simple intrinsic
alignment models: one in which the galaxy ellipticity is linearly related to
the tidal field, and one in which it is quadratic in the tidal field as
suggested by tidal torque theory. The first model predicts a
gravitational-intrinsic (GI) correlation that can be much greater than the
intrinsic-intrinsic (II) correlation for broad redshift distributions, and that
remains when galaxies pairs at similar redshifts are rejected. The second
model, in its simplest form, predicts no gravitational-intrinsic correlation.
In the first model and assuming a normalization consistent with recently
claimed detections of intrinsic correlations we find that the GI correlation
term can exceed the usual II term by >1 order of magnitude and the intrinsic
correlation induced B-mode by 2 orders of magnitude. These interference effects
can suppress the lensing power spectrum for a single broad redshift bin by of
order ~10% at z_s=1 and ~30% at z_s=0.5.

Astrophysics