New Instantons for Matrix Models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866917184000753664 |
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| author | Marino, Marcos Schiappa, Ricardo Schwick, Maximilian |
| author_facet | Marino, Marcos Schiappa, Ricardo Schwick, Maximilian |
| contents | The complete, nonperturbative content of random matrix models is described by resurgent-transseries -- general solutions to their corresponding string-equations. These transseries include exponentially-suppressed multi-instanton amplitudes obtained by eigenvalue tunneling, but they also contain exponentially-enhanced and mixed instanton-like sectors with no known matrix model interpretation. This work shows how these sectors can be also described by eigenvalue tunneling in matrix models -- but on the non-physical sheet of the spectral curve describing their large-N limit. This picture further explains the full resurgence of random matrices via analysis of all possible eigenvalue integration-contours. How to calculate these "anti" eigenvalue-tunneling amplitudes is explained in detail and in various examples, such as the cubic and quartic matrix models, and their double-scaling limit to Painleve I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13479 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | New Instantons for Matrix Models Marino, Marcos Schiappa, Ricardo Schwick, Maximilian High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems The complete, nonperturbative content of random matrix models is described by resurgent-transseries -- general solutions to their corresponding string-equations. These transseries include exponentially-suppressed multi-instanton amplitudes obtained by eigenvalue tunneling, but they also contain exponentially-enhanced and mixed instanton-like sectors with no known matrix model interpretation. This work shows how these sectors can be also described by eigenvalue tunneling in matrix models -- but on the non-physical sheet of the spectral curve describing their large-N limit. This picture further explains the full resurgence of random matrices via analysis of all possible eigenvalue integration-contours. How to calculate these "anti" eigenvalue-tunneling amplitudes is explained in detail and in various examples, such as the cubic and quartic matrix models, and their double-scaling limit to Painleve I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques. |
| title | New Instantons for Matrix Models |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2210.13479 |