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DOE OSTI · 1851274

Riemann-Hilbert correspondence and blown up surface defects

Jeong, Saebyeok·Nekrasov, Nikita
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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 N f = 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.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSDifferential and algebraic geometryIntegrable field theoriesPhysicsSupersymmetric gauge theorySupersymmetry and duality

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Jeong, Saebyeok, Nekrasov, Nikita. 2020-12-01. Riemann-Hilbert correspondence and blown up surface defects. https://doi.org/10.1007/jhep12(2020)006

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