| Abstract: |
In this talk I will discuss the recent progress on the Higgs and Coulomb branches of 3d N=4 simply-laced unitary quiver gauge theories, particularly those including multiple (adjoint) loops. A modified quiver subtraction rule that incorporates global structures, such as monodromies and Namikawa-Weyl groups, is proposed. Specifically, global information is encoded by introducing ‘decorations’ on the quiver nodes. With this subtraction rule, all possible minimal transitions on the Higgs and Coulomb branches can be identified. Additionally, the Higgs and Coulomb branches of certain unitary quivers are shown to correspond to the dual slices in the nilpotent cones of exceptional simple Lie algebras. These findings suggest a generalization to the notion of special and non-special leaves beyond the nilpotent cone and provide deeper insights into symplectic duality. |
