Enhanced Global Symmetry of N = 4 Gauge Theories in 3d

Moduli spaces of some 3d N = 4 quiver gauge theories are studied by computing the Hilbert series of their Coulomb branch. Although this had been recognized as the traditionally difficult branch to study due to quantum correction, development of monopole formula has provided a simple approach to solving the problem. Our work focuses on obtaining the global symmetry of a quiver gauge theory from its Hilbert series. Many of the quivers being studied are A,D,B Dynkin diagrams with a minimally unbalanced gauge node and the results show that their global symmetries have been enhanced to symplectic groups, corresponding to freely generated Coulomb branches. We have made an argument that simplifies the process of identifying symplectic global symmetries. A potential class of quivers is also proposed as a generalisation of some obtained results, and the quiver is compared with some previous work that takes different approaches to the problem, such as brane construction etc.. B type quivers are not included in the proposed generalisation, and its symplectic global symmetry may indicate an extension of previous work to non-simply laced quivers.