  Redshift-space distortions are a sensitive probe of the growth of large-scale
structure. In the linear regime, redshift-space distortions are fully described
by the multipoles of the two-point correlation function. In the nonlinear
regime, however, higher-order statistics are needed to capture the full
information of the galaxy density field. In this paper, we show that the
redshift-space line correlation function--which is a measure of Fourier phase
correlations--is sensitive to the nonlinear growth of the density and velocity
fields and to the nonlinear mapping between real and redshift space. We expand
the line correlation function in multipoles, and we show that almost all of the
information is encoded in the monopole, quadrupole, and hexadecapole. We argue
that these multipoles are highly complementary to the multipoles of the
two-point correlation function: first, because they are directly sensitive to
the difference between the density and the velocity coupling kernels, which is
a purely nonlinear quantity; and second, because the multipoles are
proportional to different combinations of $f$ and $\sigma_8$. Measured in
conjunction with the two-point correlation function and the bispectrum, the
multipoles of the line correlation function could therefore allow us to
disentangle efficiently these two quantities and to test modified theories of
gravity.
