One is aware that in the axial gauge (say the light-cone gauge $A_{-}=0$) non-supersymmetric Chern-Simons' theory is a quadratic theory. Hence in this gauge there are no gauge-gauge interactions. Then what is non-Abelian about this theory?
Are there effects which exist inspite of the above which make the theory different from the Abelian one?
I am aware that there are calculations of exact partition functions for Chern-Simons' theory on compact 3-manifolds. Is that the subtle point that the non-Abelian-ness will somehow manifest itself when on compact space-times? (..or on manifolds with boundary?..) That there is some reason such convenient axial gauges may not exist for compact space-times? (..though i can't see why one can't always choose $A_{-}=0$..because 3-manifolds are parallelizable there aren't any topological restrictions but there could be an issue with Gribov ambiguities..I don't know and would like to know about)
I guess that for supersymmetric Chern-Simons' theories this question itself doesn;t arise since I guess there are no gauge choices where the theory will become quadratic in the gauge fields.
(- related i would love to know of any proof/argument as to why there can't be such a gauge choice for YM theory which will make it quadratic - axial gauge can kill the quartic term but I guess thats the best one can do..)