(1) The pure gauge parts of non-Abelian Lagrangians contain self-interaction terms that are trilinear and quadrilinear in the gauge fields.
(2) Non-Abelian gauge groups have topologically non-trivial field configurations (e.g. instantons).
Are these two aspects of non-Abelian gauge groups completely unrelated or is there an intuitive connection between (1) and (2)?
For example, 't Hooft showed that fermionic zero modes in the instanton background lead to a non-perturbative multi-fermion interaction in the low energy effective action - can that somehow be related to the self-interaction in the pure gauge parts?