2021年7月
Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S1
Journal of High Energy Physics
- ,
- ,
- ,
- 巻
- 2021
- 号
- 7
- 開始ページ
- 096
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/jhep07(2021)096
- 出版者・発行元
- Springer Science and Business Media LLC
<title>A<sc>bstract</sc>
</title>We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with <italic>N</italic> minima on <italic>S</italic>1. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of <italic>N</italic>-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with ’t Hooft anomaly for even <italic>N</italic> and global inconsistency for odd <italic>N</italic>. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.
</title>We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with <italic>N</italic> minima on <italic>S</italic>1. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of <italic>N</italic>-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with ’t Hooft anomaly for even <italic>N</italic> and global inconsistency for odd <italic>N</italic>. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.
- リンク情報
- ID情報
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- DOI : 10.1007/jhep07(2021)096
- eISSN : 1029-8479
- arXiv ID : arXiv:2103.06586