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Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: The sl2 case

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Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion : The sl2 case. / Marchal, Olivier; Orantin, Nicolas.

In: Journal of Mathematical Physics, Vol. 61, No. 6, 061506, 06.2020.

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Marchal, Olivier ; Orantin, Nicolas. / Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion : The sl2 case. In: Journal of Mathematical Physics. 2020 ; Vol. 61, No. 6.

Bibtex

@article{853e81b987794d13ae9385c863b00958,
title = "Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: The sl2 case",
abstract = "In this paper, we show that it is always possible to deform a differential equation ∂xψ(x) = L(x)ψ(x) with L(x)∈sl2(C)(x) by introducing a small formal parameter h in such a way that it satisfies the topological type properties of Berg{\`e}re, Borot, and Eynard [Annales Henri Poincar{\'e} 16(12), 2713-2782 (2015)]. This is obtained by including the former differential equation in an isomonodromic system and using some homogeneity conditions to introduce h. The topological recursion is then proved to provide a formal series expansion of the corresponding tau-function whose coefficients can thus be expressed in terms of intersections of tautological classes in the Deligne-Mumford compactification of the moduli space of surfaces. We present a few examples including any Fuchsian system of sl2(C)(x) as well as some elements of Painlev{\'e} hierarchies.",
author = "Olivier Marchal and Nicolas Orantin",
year = "2020",
month = jun,
doi = "10.1063/5.0002260",
language = "English",
volume = "61",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "6",

}

RIS

TY - JOUR

T1 - Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion

T2 - The sl2 case

AU - Marchal, Olivier

AU - Orantin, Nicolas

PY - 2020/6

Y1 - 2020/6

N2 - In this paper, we show that it is always possible to deform a differential equation ∂xψ(x) = L(x)ψ(x) with L(x)∈sl2(C)(x) by introducing a small formal parameter h in such a way that it satisfies the topological type properties of Bergère, Borot, and Eynard [Annales Henri Poincaré 16(12), 2713-2782 (2015)]. This is obtained by including the former differential equation in an isomonodromic system and using some homogeneity conditions to introduce h. The topological recursion is then proved to provide a formal series expansion of the corresponding tau-function whose coefficients can thus be expressed in terms of intersections of tautological classes in the Deligne-Mumford compactification of the moduli space of surfaces. We present a few examples including any Fuchsian system of sl2(C)(x) as well as some elements of Painlevé hierarchies.

AB - In this paper, we show that it is always possible to deform a differential equation ∂xψ(x) = L(x)ψ(x) with L(x)∈sl2(C)(x) by introducing a small formal parameter h in such a way that it satisfies the topological type properties of Bergère, Borot, and Eynard [Annales Henri Poincaré 16(12), 2713-2782 (2015)]. This is obtained by including the former differential equation in an isomonodromic system and using some homogeneity conditions to introduce h. The topological recursion is then proved to provide a formal series expansion of the corresponding tau-function whose coefficients can thus be expressed in terms of intersections of tautological classes in the Deligne-Mumford compactification of the moduli space of surfaces. We present a few examples including any Fuchsian system of sl2(C)(x) as well as some elements of Painlevé hierarchies.

UR - http://www.scopus.com/inward/record.url?scp=85092731222&partnerID=8YFLogxK

U2 - 10.1063/5.0002260

DO - 10.1063/5.0002260

M3 - Journal article

AN - SCOPUS:85092731222

VL - 61

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

M1 - 061506

ER -