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 2 × 2 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 Painlevé XXXIV hierarchy.

Brezin-Gross-Witten tau function and isomonodromic deformations / Bertola, M.; Ruzza, G.. - In: COMMUNICATIONS IN NUMBER THEORY AND PHYSICS. - ISSN 1931-4523. - 13:4(2019), pp. 827-883. [10.4310/CNTP.2019.v13.n4.a4]

Brezin-Gross-Witten tau function and isomonodromic deformations

Bertola, M.;Ruzza, G.
2019

Abstract

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 2 × 2 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 Painlevé XXXIV hierarchy.
COMMUNICATIONS IN NUMBER THEORY AND PHYSICS
13
4
827
883
https://arxiv.org/abs/1812.02116
Bertola, M.; Ruzza, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/108726
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