On the Painlevé Property of Isomonodromic Deformations of Fuchsian Systems

2008 ◽  
Vol 101 (1-3) ◽  
pp. 255-263 ◽  
Author(s):  
Vladimir Poberezhny
Keyword(s):  
Isomonodromic Deformations ◽  
Painlevé Property ◽  
Fuchsian Systems

scholarly journals Riemann-Hilbert correspondence and blown up surface defects

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Saebyeok Jeong ◽  
Nikita Nekrasov
Keyword(s):  
Surface Defects ◽  
Topological String ◽  
Vacuum Expectation ◽  
Companion Paper ◽  
Horizontal Section ◽  
Isomonodromic Deformations ◽  
Fuchsian Systems ◽  
Supersymmetric Gauge ◽  
Relationship Of ◽  
The Relationship

Abstract The relationship of two dimensional quantum field theory and isomonodromic deformations of Fuchsian systems has a long history. Recently four-dimensional N = 2 gauge theories joined the party in a multitude of roles. In this paper we study the vacuum expectation values of intersecting half-BPS surface defects in SU(2) theory with Nf = 4 fundamental hypermultiplets. We show they form a horizontal section of a Fuchsian system on a sphere with 5 regular singularities, calculate the monodromy, and define the associated isomonodromic tau-function. Using the blowup formula in the presence of half-BPS surface defects, initiated in the companion paper, we obtain the GIL formula, establishing an unexpected relation of the topological string/free fermion regime of supersymmetric gauge theory to classical integrability.

scholarly journals Circular quiver gauge theories, isomonodromic deformations and $$W_N$$ fermions on the torus

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Pavlo Gavrylenko ◽  
Alessandro Tanzini
Keyword(s):  
Integrable System ◽  
Gauge Theories ◽  
The Self ◽  
Free Fermion ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Specific Time ◽  
Dimensional Torus ◽  
Isomonodromic Deformations ◽  
Deformation Problem

AbstractWe study the relation between class $$\mathcal {S}$$ S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual $$\Omega $$ Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding $$\tau $$ τ -function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to $$W_N$$ W N free fermion correlators on the torus.

scholarly journals Rigid Fuchsian Systems in 2-Dimensional Conformal Field Theories

2018 ◽  
Vol 365 (1) ◽  
pp. 17-60 ◽  
Author(s):  
Vladimir Belavin ◽  
Yoshishige Haraoka ◽  
Raoul Santachiara
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Fuchsian Systems
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