Complex Langevin results in one- and two-dimensional toy models match a linear combination of integration cycles when boundary terms vanish, and the kernel choice controls which cycles contribute.
However, as is known since [62], the introduction of a nontrivial kernel K ≈ λ−1/2 in (4) can ensure ⟨zn⟩CL = ⟨zn⟩exact for arbitrary λ ̸= 0
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The Role of Integration Cycles in Complex Langevin Simulations
Complex Langevin results in one- and two-dimensional toy models match a linear combination of integration cycles when boundary terms vanish, and the kernel choice controls which cycles contribute.