Idea is to consider \(3d\) \(N=4\) quiver gauge theory.
Poincare groups gives super Poincare algebras
Higgs branch: classical, no quantum correction, hyperkahler
Coulomb branch: quantum, very difficult.
They are symplectic singularities
\(X\) is normal poisson,
there exists \(U\subset X\), .. cone
there exists \(\pi:\tilde{X}\to X\) such that \(\pi^*\omega\) has no poles on \(\tilde{X}\).
\(X\) is affine
there exists a \(\mathbb{C}^*\) action that contracts \(X\) to a point.