Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality

We employ the protected sphere correlation functions of three-dimensional Super Conformal Field Theories with eight supercharges in order to define a quantization of their Higgs and Coulomb branches of vacua as real phase spaces. We also employ hemisphere correlation functions to define a quantization of certain real loci in the Higgs and Coulomb branches. Localization formulae and dualities applied to these quantizations result in a body of …