Picard-Lefschetz theory and alien calculus: a case study
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| Format: | Preprint |
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2026
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| _version_ | 1866913106691620864 |
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| author | Li, Si Li, Yong Tang, Xinxing |
| author_facet | Li, Si Li, Yong Tang, Xinxing |
| contents | We compare Picard--Lefschetz theory and resurgence in three basic one-dimensional exponential integrals: the Airy model, the Bessel model, and the Gamma model. On the Picard--Lefschetz side, we describe the Lefschetz thimbles and compute the connecting trajectories between critical points appearing at Stokes phases. On the resurgent side, we analyze the Borel singularities of the saddle expansions and use alien operators to recover the same Stokes coefficients. These examples serve as explicit finite-dimensional test cases for the dictionary between thimble wall-crossing and alien calculus. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_08867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Picard-Lefschetz theory and alien calculus: a case study Li, Si Li, Yong Tang, Xinxing Mathematical Physics High Energy Physics - Theory Complex Variables We compare Picard--Lefschetz theory and resurgence in three basic one-dimensional exponential integrals: the Airy model, the Bessel model, and the Gamma model. On the Picard--Lefschetz side, we describe the Lefschetz thimbles and compute the connecting trajectories between critical points appearing at Stokes phases. On the resurgent side, we analyze the Borel singularities of the saddle expansions and use alien operators to recover the same Stokes coefficients. These examples serve as explicit finite-dimensional test cases for the dictionary between thimble wall-crossing and alien calculus. |
| title | Picard-Lefschetz theory and alien calculus: a case study |
| topic | Mathematical Physics High Energy Physics - Theory Complex Variables |
| url | https://arxiv.org/abs/2605.08867 |