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.
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On leave of absence from: CAS Skoltech and IITP RAS, Moscow, Russia (Nikita Nekrasov).
ArXiv ePrint: 2007.03660
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Jeong, S., Nekrasov, N. Riemann-Hilbert correspondence and blown up surface defects. J. High Energ. Phys. 2020, 6 (2020). https://doi.org/10.1007/JHEP12(2020)006
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DOI: https://doi.org/10.1007/JHEP12(2020)006