<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>SU</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> natural inflation

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