$c_{\text{eff}}$ for 3d $\mathcal{N}=2$ theories

TL;DR

This paper introduces a new quantity analogous to the effective central charge for 3d $ abla=2$ theories, based on superconformal index behavior, and explores its properties and computation methods across various theories.

Contribution

It proposes a novel effective charge concept for 3d $ abla=2$ theories and discusses its properties and calculation approaches in different models.

Findings

The proposed quantity behaves as an effective central charge in 3d $ abla=2$ theories.

Computable in both Lagrangian and strongly coupled theories.

Provides insights into the structure of 3d superconformal theories.

Abstract

Based on the observed behavior of the superconformal index in three-dimensional $\mathcal{N}=2$ theories, we propose a quantity that can be considered as an analogue of the "effective central charge." We discuss the general properties of this quantity and ways of computing it in a variety of different theories, including simple Lagrangian theories as well as more interesting strongly coupled examples that come from 3d-3d correspondence.