# New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling

## TL;DR

This paper constructs new 3d $ ext{N}=2$ superconformal field theories with $N^{3/2}$ scaling, matching geometric volumes from free energy and Hilbert series, and explores their potential M-theory duals.

## Contribution

It introduces novel 3d $ ext{N}=2$ models with $N^{3/2}$ scaling and establishes connections with their geometric duals via volume matching.

## Key findings

- New 3d $ ext{N}=2$ models with $N^{3/2}$ scaling
- Matching volumes from free energy and Hilbert series
- Existence of Sasaki-Einstein metrics on internal spaces

## Abstract

We construct several novel examples of 3d $\mathcal{N}=2$ models whose free energy scales as $N^{3/2}$ at large $N$. This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d parents of the 3d models, matching the volume extracted from the $a$ conformal anomaly to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.