SO and USp (Hyper)Kahler Quotients and Lumps

The properties of supersymmetric gauge theories in the Higgs phase at low energies can appropriately be studied by means of a non-linear sigma model, which has the target space being Kahler for N=1 supersymmetric models and hyperKahler for N=2 models. By construction of the Kahler and hyperKahler quotients for the gauge theories with SO and USp gauge symmetries, we obtain the explicit metrics on their respective manifolds. Furthermore, we study the lumps in the non-linear sigma models and their effective description, using the Kahler quotients.