Sign optimization and complex saddle points in one-dimensional QCD

We study one-dimensional QCD at finite quark density by using the sign optimization framework. The fermion problem is mitigated deforming path integral domain, $SU(3)$ to a complexified one ${\cal M} \subset SL(3)$, explicitly constructed reduce phase fluctuations. complexification angular representation of $SU(3)$. provide physical explanation procedure in terms complex saddle points. This picture connects framework generalized Lefschetz thimbles.