# Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

## TL;DR

This paper classifies all rank 2 orbifold geometries related to four-dimensional al theories with al al al supersymmetry, revealing known and potentially new exotic al theories.

## Contribution

It provides a comprehensive classification of al moduli space orbifolds at rank 2, identifying six geometries not associated with known theories.

## Key findings

- Most geometries correspond to known or discretely gauged theories.
- Six geometries are novel and not realized by existing theories.
- Three of these have non-freely generated Coulomb branch slices, indicating new al theories.

## Abstract

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an $\mathcal{N}=2$ Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic $\mathcal{N}=3$ theories.