Quiver Gauge Theories

The student will study the geometry and the related physics of Coulomb and Higgs branches of certain supersymmetric field theories in three dimensions. The main tools will be the considerations of nilpotent orbits and string theory brane configurations. Changes in brane configurations are mapped into Kraft-Procesi transitions which connect various nilpotent orbits. The moduli spaces of three dimensional theories are connect to moduli spaces of five and six dimensional theories so relevant information could be collected about the later theories. The student will study supersymmetric field theories in dimensions between three and six. He will continue by getting familiar with quiver gauge theories of good, bad and ugly type, depending on the rank of the gauge group and the number of fundamental flavours. A thorough study of string theory will be required, with emphasis on aspects like brane configurations and their associated field theories. The final goal is to describe in detail quiver gauge theories which were not explored in the past like the ones for non simply laced quivers or E type quivers, together with relations to higher dimensional theories.