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.
Highlights
The rich physics of four-dimensional N = 2 supersymmetric gauge theories is sometimes encoded in the intricate ways in the geometry of the moduli space of vacua
The surface defect observables O1 and O2 reduce to generalized hypergeometric functions, which are partition functions of the two-dimensional gauged linear sigma model on the Hom(O(−1), CN )-bundle over PN−1 whose Kähler modulus is q1 and q3, respectively
In the presence of half-BPS surface defects, the qq-characters are especially powerful since they lead to closed differential equations satisfied by the partition functions in many cases [23, 24, 31], which can be regarded as double quantization of the chiral ring relation of the coupled system
Summary
Where z denotes the complexified FI parameter of the gauged linear sigma model of the defect on the z2-plane This blowup formula contains rich analytic information on the surface defect partition function, just as the previous one without the defect does for the. This is mainly re-phrasing the result of [12] in purely gauge theoretical terms.
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