SU($N$)-natural inflation
  We study SU($N$) gauge fields that couple to the inflaton through the
Chern-Simons term. We provide a general procedure to construct homogeneous,
isotropic, and attractor solutions of the gauge fields during inflation. The
gauge fields develop various VEVs corresponding to different spontaneous
symmetry breaking patterns of SU($N$) where embedded SU($2$) subgroups are
broken with the spatial rotation SO($3$) symmetry. As specific examples, we
construct the stable solutions for $N = 3$ and $4$. We also numerically solve
the gauge field dynamics and confirm that our analytic solutions are complete
and attractor. It is straightforward to apply our procedure to the other simple
Lie groups.
