We study the SU(N) gauge fields coupled with the inflaton through the Chern-Simons coupling and propose a general procedure for constructing homogeneous, isotropic, and attractor solutions of the gauge fields during inflation. Gauge fields develop various vacuum expectation values 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 numerically solve the gauge field dynamics and confirm that our analytic solutions are complete and act as attractors. Notably, the proposed approach is applicable to the other simple Lie groups.
ASJC Scopus subject areas