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Some remarks on Lefschetz thimbles and complex Langevin dynamics

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arxiv 1407.2090 v2 pith:3IKBAS4V submitted 2014-07-08 hep-lat hep-th

Gert Aarts , Lorenzo Bongiovanni , Erhard Seiler , Denes Sexty This is my paper · ORCID
classification hep-lathep-th
keywords complexdynamicslangevinsomethimblesfindfixedlefschetz
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Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U(1) and SU(2) models in the presence of a determinant, which have some features not discussed before, due to a singular drift. We find evidence for a relation between classical runaways and stable thimbles, and give an example of a degenerate fixed point. We typically find that the distributions sampled in complex Langevin dynamics are related to the thimble(s), but with some important caveats, for instance due to the presence of unstable fixed points in the Langevin dynamics.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Designing weight regularizations based on Lefschetz thimbles to stabilize complex Langevin

    hep-lat 2024-12 conditional novelty 7.0 of 10

    A regularization inspired by Lefschetz thimbles stabilizes complex Langevin simulations in toy models, with a bias-correction step that restores the original expectation values.

  2. Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW

    hep-th 2025-07 unverdicted novelty 6.0 of 10

    Exact Airy-function evaluation of the Gauss-Bonnet mini-superspace path integral plus Picard-Lefschetz resolution of lapse degeneracies via complex (G ħ) deformation that alters the KSW condition.

  3. The Role of Integration Cycles in Complex Langevin Simulations

    hep-lat 2024-12 conditional novelty 6.0 of 10

    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.

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