Sheaf quantization from exact WKB analysis
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866929352434778112 |
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| author | Kuwagaki, Tatsuki |
| author_facet | Kuwagaki, Tatsuki |
| contents | A sheaf quantization is a sheaf associated to a Lagrangian brane. By using the results of exact WKB analysis, we sheaf-quantize spectral curves over the Novikov ring under some assumptions on the behavior of Stokes curves. For Schrödinger equations, we prove that the local system associated to the sheaf quantization (microlocalization a.k.a. abelianization) over the spectral curve can be identified with the Voros--Iwaki--Nakanishi coordinate. We expect that these sheaf quantizations are the object-level realizations of the $\hbar$-enhanced Riemann--Hilbert correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_14872 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sheaf quantization from exact WKB analysis Kuwagaki, Tatsuki Symplectic Geometry High Energy Physics - Theory Algebraic Geometry Quantum Algebra A sheaf quantization is a sheaf associated to a Lagrangian brane. By using the results of exact WKB analysis, we sheaf-quantize spectral curves over the Novikov ring under some assumptions on the behavior of Stokes curves. For Schrödinger equations, we prove that the local system associated to the sheaf quantization (microlocalization a.k.a. abelianization) over the spectral curve can be identified with the Voros--Iwaki--Nakanishi coordinate. We expect that these sheaf quantizations are the object-level realizations of the $\hbar$-enhanced Riemann--Hilbert correspondence. |
| title | Sheaf quantization from exact WKB analysis |
| topic | Symplectic Geometry High Energy Physics - Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2006.14872 |