Exact multi-instantons in topological string theory
Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series...
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| Format: | Article |
| Language: | English |
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SciPost
2023-10-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.4.179 |
| _version_ | 1827782746301267968 |
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| author | Jie Gu, Marcos Mariño |
| author_facet | Jie Gu, Marcos Mariño |
| author_sort | Jie Gu, Marcos Mariño |
| collection | DOAJ |
| description | Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series extension of the BCOV holomorphic anomaly equations. In this paper we find exact, closed form solutions for these multi-instanton trans-series in the case of local Calabi-Yau manifolds. The resulting multi-instanton amplitudes turn out to be very similar to the eigenvalue tunneling amplitudes of matrix models. Their form suggests that the flat coordinates of the Calabi-Yau manifold are naturally quantized in units of the string coupling constant, as postulated in large $N$ dualities. Based on our results we obtain a general picture for the resurgent structure of the topological string in the local case, which we illustrate with explicit calculations for local $\mathbb{P}^2$. |
| first_indexed | 2024-03-11T15:37:27Z |
| format | Article |
| id | doaj.art-a9521710951d40f092e3e69dc3f89ca0 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-11T15:37:27Z |
| publishDate | 2023-10-01 |
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| record_format | Article |
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| spelling | doaj.art-a9521710951d40f092e3e69dc3f89ca02023-10-26T15:50:25ZengSciPostSciPost Physics2542-46532023-10-0115417910.21468/SciPostPhys.15.4.179Exact multi-instantons in topological string theoryJie Gu, Marcos MariñoTopological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series extension of the BCOV holomorphic anomaly equations. In this paper we find exact, closed form solutions for these multi-instanton trans-series in the case of local Calabi-Yau manifolds. The resulting multi-instanton amplitudes turn out to be very similar to the eigenvalue tunneling amplitudes of matrix models. Their form suggests that the flat coordinates of the Calabi-Yau manifold are naturally quantized in units of the string coupling constant, as postulated in large $N$ dualities. Based on our results we obtain a general picture for the resurgent structure of the topological string in the local case, which we illustrate with explicit calculations for local $\mathbb{P}^2$.https://scipost.org/SciPostPhys.15.4.179 |
| spellingShingle | Jie Gu, Marcos Mariño Exact multi-instantons in topological string theory SciPost Physics |
| title | Exact multi-instantons in topological string theory |
| title_full | Exact multi-instantons in topological string theory |
| title_fullStr | Exact multi-instantons in topological string theory |
| title_full_unstemmed | Exact multi-instantons in topological string theory |
| title_short | Exact multi-instantons in topological string theory |
| title_sort | exact multi instantons in topological string theory |
| url | https://scipost.org/SciPostPhys.15.4.179 |
| work_keys_str_mv | AT jiegumarcosmarino exactmultiinstantonsintopologicalstringtheory |