  Non-Abelian gauge fields are versatile tools for synthesizing topological
phenomena but have so far been mostly studied in Hermitian systems, where gauge
flux has to be defined from a closed loop in order for gauge fields, whether
Abelian or non-Abelian, to become physically meaningful. We show that this
condition can be relaxed in non-Hermitian systems by proposing and studying a
generalized Hatano--Nelson model with imbalanced non-Abelian hopping. Despite
lacking gauge flux in one dimension, non-Abelian gauge fields create rich
non-Hermitian topological consequences. Under only nearest-neighbor coupling,
non-Abelian gauge fields enable Hopf-link bulk braiding topology, whose phase
transition accompanies the emergence of exceptional points (EPs). At both ends
of an open chain, non-Abelian gauge fields lead to the simultaneous presence of
non-Hermitian skin modes, whose population can be effectively tuned. Asymptotic
analysis shows that this tuning mechanism stems from the interplay between the
Abelian Hatano--Nelson coupling and effective high-order hopping, which becomes
substantial near the EP phase transition condition. The predicted non-Hermitian
phenomena, enabled by non-Abelian gauge fields, could be realized in synthetic
dimensional optical platforms such as time-multiplexed photonic mesh lattices
and driven ring resonators.
