Seiberg-Witten Geometry of Four-Dimensional = 2 Quiver Gauge Theories - Nekrasov, Nikita; Pestun, Vasily (Symmetry, Integrability and Geometry: Methods and Applications, 2023)
Seiberg-Witten geometry of mass deformed = 2 superconformal ADE quiver gauge theories in four dimensions is determined. We solve the limit shape equations derived from the gauge theory and identify the space of vacua of the theory with the moduli space of the genus zero holomorphic (quasi)maps to the moduli space BunG(ℰ) of holomorphic ℂ-bundles on a (possibly degenerate) elliptic curve ℰ defined in terms of the microscopic gauge couplings, for the corresponding simple ADE Lie group . The integrable systems underlying the special geometry of are identified. The moduli spaces of framed -instantons on ℝ²×², of -monopoles with singularities on ℝ²×¹, the Hitchin systems on curves with punctures, as well as various spin chains play an important rôle in our story. We also comment on the higher-dimensional theories.