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

Understand

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.