Riemann-Hilbert correspondence and blown up surface defects

Understand

The relationship of two dimensional quantum field theory and isomonodromic deformations of Fuchsian systems has a long history.

• Recently four-dimensional $\mathcal{N}=2$ 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.