Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics

[2602.20576] Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics Skip to main content Search Submit Donate Log in High Energy Physics - Theory arXiv:2602.20576 (hep-th) [Submitted on 24 Feb 2026 ( v1 ), last revised 25 Aug 2026 (this version, v3)] Title: Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics Authors: Jie Gu , Marcos Marino View PDF HTML (experimental) Abstract: The quantization of the Seiberg-Witten curve of ${\cal N}=2$ super Yang-Mills theory leads to a deformation of one-dimensional quantum mechanics with unconventional behavior. Most notably, quantum tunneling is suppressed at special points in parameter space. In this paper we examine these deformed models in the case of double-well and cubic potentials, and we find that they have a rich phase structure. In what we call the strong coupling phase, the theory behaves like conventional quantum mechanics, instantons are real, and tunneling is not suppressed. In the weak coupling phase, the instantons responsible for tunneling become complex, and tunneling suppression takes place at the so-called Toda lattice points. At the critical point between the two phases, which corresponds to a monopole point in super Yang-Mills theory, the non-perturbative amplitudes display an anomalous scaling as a function of $\hbar$. This phase structure reflects the physics of the underlying super Yang-Mills theory and can be regarded as a physical manifestation of wall-crossing behavior of the BPS spectrum, which we determine in our problem by using resurgent techniques. Comments: 42 pages, 18 figures, typos corrected Subjects: High Energy Physics - Theory (hep-th) Cite as: arXiv:2602.20576 [hep-th] (or arXiv:2602.20576v3 [hep-th] for this version) https://doi.org/10.48550/arXiv.2602.20576 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jie Gu [ view email ] [v1] Tue, 24 Feb 2026 05:58:59 UTC (1,483 KB) [v2] Thu, 7 May 2026 04:31:45 UTC (1,513 KB) [v3] Tue, 25 Aug 2026 01:22:27 UTC (1,509 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-02 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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