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We present our latest results on the application of the complex Langevinmethod to one- and two-dimensional QCD. Although the method is stable, itunfortunately converges to an incorrect result when applied as such. Afterapplying additional gauge cooling steps, the results agree with the knownanalytical results in the one-dimensional case. However, in the two-dimensionalcase the disagreement subsists, even with gauge cooling, when the sign problemis sufficiently large.

Complex Langevin in low-dimensional QCD: the good and the not-so-good