Speaker
Description
This is a minireview devoted to the problem of vacuum dynamics in $3d$
supersymmetric Yang-Mills-Chern-Simons theories with and without extra
matter multiplets. Performing an explicit analysis of the effective Born-Oppenheimer Hamiltonian in a small spatial box, we calculate the number of vacuum states (the Witten index) for these theories and analyze their structure.
The method of this study is similar to the method developped by Witten for 4-dimensional supersymmetric gauge theories, but 3-dimensional theories turn out to be more complicated and their dynamics involves interesting non-trivialities. In particular: (i) the tree-level effective Hamiltonian is not just a free Laplacian, but involves an extra homogeneous magnetic field, (ii) it is not enough to analyze the effecive Hamiltonian to the leading BO order, but one-loop corrections should also be taken into account.
