Gauge Theory and Symplectic Duality

Symplectic duality is an equivalence of mathematical structures associated to pairs of hyper-Kahler cones. All known examples arise as the `Higgs branch’ and `Coulomb branch' of a 3d superconformal quantum field theory. In particular, there is a rich class of examples where the Higgs branch is a Nakajima quiver variety and the Coulomb branch is a moduli spaceof singular magnetic monopoles. In this case, I will show that the equivariant cohomology of the moduli space of based quasi-maps to the Higgs branch transforms as a Verma module for the deformation quantisation of the Coulomb branch