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Summing up perturbation series around superintegrable point
- Source :
- Phys.Lett. B852 (2024) 138593
- Publication Year :
- 2024
-
Abstract
- 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.<br />Comment: 15 pages + Appendix (7 pages)
- Subjects :
- High Energy Physics - Theory
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys.Lett. B852 (2024) 138593
- Publication Type :
- Report
- Accession number :
- edsarx.2401.14392
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.physletb.2024.138593