Flavor Symmetries and Unitarity Bounds in $\mathcal{N}=2$ Superconformal Field Theories

In this Letter I analyze the constraints imposed by unitarity on the flavor central charges of four-dimensional $\mathcal{N}=2$ superconformal field theories with general reductive global symmetry groups. I derive several general and far-reaching consequences of unitarity by computing the norms of flavor singlet Higgs branch operators appearing in the squares of “moment map” operators via the associated vertex operator algebra, and imposing the requirement that they be non-negative.