Riemann-Hilbert correspondence and blown up surface defects

Saebyeok Jeong, Nikita Nekrasov

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Article number6
JournalJournal of High Energy Physics
Issue number12
Publication statusPublished - Dec 2020
Externally publishedYes


  • Differential and Algebraic Geometry
  • Integrable Field Theories
  • Supersymmetric Gauge Theory
  • Supersymmetry and Duality


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