On the resurgent structure of quantum periods
Quantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be described in terms of topological string free energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We consider the trans-series extension of the holomorphic anomaly equations sati...
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| Format: | Article |
| Language: | English |
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SciPost
2023-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.1.035 |
| _version_ | 1797770707489259520 |
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| author | Jie Gu, Marcos Mariño |
| author_facet | Jie Gu, Marcos Mariño |
| author_sort | Jie Gu, Marcos Mariño |
| collection | DOAJ |
| description | Quantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be described in terms of topological string free energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We consider the trans-series extension of the holomorphic anomaly equations satisfied by these quantities, and we obtain exact multi-instanton solutions for these trans-series. Building on this result, we propose a unified perspective on the resurgent structure of quantum periods. We show for example that the Delabaere-Pham formula, which was originally obtained in quantum mechanical examples, is a generic feature of quantum periods. We illustrate our general results with explicit calculations for the double-well in quantum mechanics, and for the quantum mirror curve of local $\mathbb{P}^2$. |
| first_indexed | 2024-03-12T21:27:04Z |
| format | Article |
| id | doaj.art-de13ca40f8f04b17ad611627862d44c7 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-12T21:27:04Z |
| publishDate | 2023-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-de13ca40f8f04b17ad611627862d44c72023-07-28T07:12:09ZengSciPostSciPost Physics2542-46532023-07-0115103510.21468/SciPostPhys.15.1.035On the resurgent structure of quantum periodsJie Gu, Marcos MariñoQuantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be described in terms of topological string free energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We consider the trans-series extension of the holomorphic anomaly equations satisfied by these quantities, and we obtain exact multi-instanton solutions for these trans-series. Building on this result, we propose a unified perspective on the resurgent structure of quantum periods. We show for example that the Delabaere-Pham formula, which was originally obtained in quantum mechanical examples, is a generic feature of quantum periods. We illustrate our general results with explicit calculations for the double-well in quantum mechanics, and for the quantum mirror curve of local $\mathbb{P}^2$.https://scipost.org/SciPostPhys.15.1.035 |
| spellingShingle | Jie Gu, Marcos Mariño On the resurgent structure of quantum periods SciPost Physics |
| title | On the resurgent structure of quantum periods |
| title_full | On the resurgent structure of quantum periods |
| title_fullStr | On the resurgent structure of quantum periods |
| title_full_unstemmed | On the resurgent structure of quantum periods |
| title_short | On the resurgent structure of quantum periods |
| title_sort | on the resurgent structure of quantum periods |
| url | https://scipost.org/SciPostPhys.15.1.035 |
| work_keys_str_mv | AT jiegumarcosmarino ontheresurgentstructureofquantumperiods |