Typicality, Black Hole Microstates and Superconformal Field Theories

We analyze the structure of heavy multitrace BPS operators in N = 1 superconformal quiver gauge theories that arise on the worldvolume of D3-branes on an affine toric cone. We exhibit a geometric procedure for counting heavy mesonic operators with given U(1) charges. We show that for any fixed linear combination of the U(1) charges, the entropy is maximized when the charges are in certain ratios. This selects preferred directions in the charge space that can be determined with the help of a piece of string. We show that almost all heavy mesonic operators of fixed U(1) charges share a universal structure. This universality reflects the properties of the dual extremal black holes whose microstates they create. We also interpret our results in terms of typical configurations of dual giant gravitons in AdS space.