Vacuum structure in 3D supersymmetric gauge theories

Based on a talk given at the Pomeranchuk memorial conference at ITEP in June 2013, we review the vacuum dynamics„ in 3d supersymmetric Yang–Mills–Chern–Simons theories with and without extra matter multiplets. By analyzing the effective Born–Oppenheimer Hamiltonian in a small spatial box, we calculate the number of vacuum states (Witten index) and examine their structure for these theories. The results are identical to those obtained by other methods.