Brezin-Gross-Witten tau function and isomonodromic deformations

被引：0

作者：

Bertola, Marco ^{[1
,2
,3
]}

Ruzza, Giulio ^{[3
]}

机构：

[1] Concordia Univ, Dept Math & Stat, 1455 De Maisonneuve W, Montreal, PQ H3G 1M8, Canada

[2] Univ Montreal, Ctr Rech Math, CP 6128,Succ Ctr Ville, Montreal, PQ H3C 3J7, Canada

[3] Scuola Int Super Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy

来源：

COMMUNICATIONS IN NUMBER THEORY AND PHYSICS | 2019年 / 13卷 / 04期

基金：

欧盟地平线“2020”; 加拿大自然科学与工程研究理事会;

关键词：

Brezin-Gross-Witten tau function; isomonodromic deformations; Painleve XXXIV hierarchy; Norbury classes; ORDINARY DIFFERENTIAL-EQUATIONS; EXTERNAL-FIELD; TRANSFORMATIONS; UNITARY; HIERARCHY; INTEGRALS; SPECTRUM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Brezin-Gross-Witten tau function is a tau function of the KdV hierarchy which arises in the weak coupling phase of the Brezin-Gross-Witten model. It falls within the family of generalized Kontsevich matrix integrals, and its algebro-geometric interpretation has been unveiled in recent works of Norbury. This tau function admits a natural extension, called generalized Brezin-Gross-Witten tau function. We prove that the latter is the isomonodromic tau function of a 2x2 isomonodromic system and consequently present a study of this tau function purely by means of this isomonodromic interpretation. Within this approach we derive effective formulae for the generating functions of the correlators in terms of simple generating series, the Virasoro constraints, and discuss the relation with the Painleve XXXIV hierarchy.

引用

页码：827 / 883

页数：57