Hanany, Amihay2016-05-172016-05-172016-05-12https://hdl.handle.net/11299/180334Theories with 8 supercharges have moduli spaces of vacua which generically divide into two branches - the so called Coulomb branch and the Higgs branch. These branches are HyperKahler in the cases of Higgs branch in dimensions 3 up to 6, and Coulomb branch in 3. They become cones when one sets the FI terms and masses to zero. There is a natural SU(2)_R which acts on 3 complex structures. We will devote our talk to general aspects of HyperKahler cones and discuss quiver gauge theories where these spaces arise as moduli spaces in one or more of these branches. Special attention is given to moduli spaces in which the generators of the chiral carry spin 1 under SU(2)_R, and consequently transform in the adjoint representation of the global symmetry group. They shall be termed mesonic moduli spaces. It turns out that there is a full classification of these spaces which goes under the name of “nilpotent orbits”. We will discuss general aspects of these spaces and the new exciting directions that these results can take us.enFTPIQCDPresentation