Riemann-Hilbert correspondence and blown up surface defects

Saebyeok Jeong, Nikita Nekrasov
2020 Journal of High Energy Physics  
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
more » ... 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.
doi:10.1007/jhep12(2020)006 fatcat:7y5g6crxm5cu5iayc4ieobpxpu