# Comments on flavor symmetry breaking and three-dimensional superconformal index

## TL;DR

This paper studies the superconformal index of a 3D supersymmetric QCD with flavor symmetry breaking, showing how the index vanishes generally but reveals symmetry breaking at special fugacity values.

## Contribution

It provides a method to derive the index for a theory with fewer flavors by integrating out a flavor from a higher-flavor theory, highlighting symmetry-breaking effects.

## Key findings

- Index vanishes for generic fugacities
- Special fugacity choices reveal flavor symmetry breaking
- Method to obtain lower-flavor index from higher-flavor theory

## Abstract

We investigate the superconformal index of a three-dimensional $SU(2)$ ${\mathcal N}=2$ supersymmetric QCD with $N_f=4$ flavors. This theory confines with the breaking of a global symmetry. We obtain the index of this theory by integrating out a flavor from the theory with $N_f=6$ flavors. The superconformal index of the theory vanishes for generic values of the flavor fugacities. However, the specific choice of fugacities allows us to describe the flavor symmetry-breaking phenomenon.