تقرير
Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
| العنوان: | Deformation of superintegrability in the Miwa-deformed Gaussian matrix model |
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| المؤلفون: | Mironov, A., Morozov, A., Popolitov, A., Shakirov, Sh. |
| المصدر: | Phys. Rev. D 110 (2024) 046027 |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematical Physics |
| الوصف: | We consider an arbitrary deformation of the Gaussian matrix model parameterized by Miwa variables $z_a$. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is not, still one can find an explicit expression for an arbitrary Schur average as a linear transform of a {\it finite degree} polynomial made from the values of skew Schur functions at the Gaussian locus $p_k=\delta_{k,2}$. This linear operation includes multiplication with an exponential $ e^{z_a^2/2}$ and a kind of Borel transform of the resulting product, which we call multiple and enhanced. The existence of such remarkable formulas appears intimately related to the theory of auxiliary $K$-polynomials, which appeared in {\it bilinear} superintegrable correlators at the Gaussian point (strict superintegrability). We also consider in the very detail the generating function of correlators $<(\Tr X)^k>$ in this model, and discuss its integrable determinant representation. At last, we describe deformation of all results to the Gaussian $\beta$-ensemble. Comment: 21 pages. arXiv admin note: text overlap with arXiv:2401.14392 |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevD.110.046027 |
| URL الوصول: | http://arxiv.org/abs/2403.09670 |
| رقم الأكسشن: | edsarx.2403.09670 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevD.110.046027 |
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