Summing up perturbation series around superintegrable point
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909166367408128 |
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| author | Mironov, A. Morozov, A. Popolitov, A. Shakirov, Sh. |
| author_facet | Mironov, A. Morozov, A. Popolitov, A. Shakirov, Sh. |
| contents | We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on the example of a single Miwa variable. The ordinary Gaussian model is superintegrable, i.e. the average of the Schur functions $S_Q$ is an explicit function of the Young diagram $Q$. The question is what happens to this property after perturbation. We show that the entire perturbation series can be nicely summed up into a kind of Borel transform of a universal exponential function, while the dependence on $R$ enters through a polynomial factor in front of this exponential. Moreover, these polynomials can be described explicitly through a single additional structure, which we call ``truncation'' of the Young diagram $Q$. It is unclear if one can call this an extended superintegrability, but at least it is a tremendously simple deformation of it. Moreover, the vanishing Gaussian correlators remain vanishing and, hence, are not deformed at all. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_14392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Summing up perturbation series around superintegrable point Mironov, A. Morozov, A. Popolitov, A. Shakirov, Sh. High Energy Physics - Theory Mathematical Physics We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on the example of a single Miwa variable. The ordinary Gaussian model is superintegrable, i.e. the average of the Schur functions $S_Q$ is an explicit function of the Young diagram $Q$. The question is what happens to this property after perturbation. We show that the entire perturbation series can be nicely summed up into a kind of Borel transform of a universal exponential function, while the dependence on $R$ enters through a polynomial factor in front of this exponential. Moreover, these polynomials can be described explicitly through a single additional structure, which we call ``truncation'' of the Young diagram $Q$. It is unclear if one can call this an extended superintegrability, but at least it is a tremendously simple deformation of it. Moreover, the vanishing Gaussian correlators remain vanishing and, hence, are not deformed at all. |
| title | Summing up perturbation series around superintegrable point |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2401.14392 |