# Flavor symmetries and unitarity bounds in ${\mathcal N}=2$ SCFTs

## TL;DR

This paper investigates how unitarity constraints limit the flavor central charges in 4D ${\mathcal N}=2$ SCFTs, deriving broad implications through vertex operator algebra techniques.

## Contribution

It introduces a method to derive unitarity bounds on flavor central charges using vertex operator algebra and Higgs branch operator norms.

## Key findings

- Unitarity imposes non-negativity constraints on operator norms.
- Derived bounds on flavor central charges for various symmetry groups.
- Established general consequences for ${\mathcal N}=2$ SCFTs.

## Abstract

In this letter I analyze the constraints imposed by unitarity on the flavor central charges of four-dimensional ${\mathcal N}=2$ SCFTs 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.