The moduli spaces of 3d N≥ 2 Chern-Simons gauge theories and their Hilbert series

We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d N≥ 2 Yang-Mills-Chern-Simons theories. The formula counts ’t Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperKähler twofold singularities with N≥ 2 and N≥ 3 supersymmetry.