The work of Andrey Bolibrukh on isomonodromic deformations

2009 ◽  
pp. 9-25
Author(s):  
Claude Sabbah
Keyword(s):  
Isomonodromic Deformations

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 Isomonodromic Deformations and Very Stable Vector Bundles of Rank Two

2017 ◽  
Vol 356 (2) ◽  
pp. 627-640 ◽  
Author(s):  
Indranil Biswas ◽  
Viktoria Heu ◽  
Jacques Hurtubise
Keyword(s):  
Vector Bundles ◽  
Isomonodromic Deformations ◽  
Stable Vector Bundles
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