# Three dimensional canonical singularity and five dimensional N=1 SCFT

## TL;DR

This paper proposes a correspondence between three-dimensional canonical singularities and five-dimensional N=1 SCFTs, linking singularity structures to flavor symmetries and Coulomb branch geometry.

## Contribution

It introduces a conjecture connecting singularity types to 5D SCFTs and describes how Coulomb branch structure is derived from crepant resolutions and their Nef cones.

## Key findings

- Non-abelian flavor symmetry from singularity type
- Coulomb branch dimension from crepant divisors
- Coulomb chamber structure from crepant resolution fan

## Abstract

We conjecture that every three dimensional canonical singularity defines a five dimensional N=1 SCFT. Flavor symmetry can be found from singularity structure: non-abelian flavor symmetry is read from the singularity type over one dimensional singular locus. The dimension of Coulomb branch is given by the number of compact crepant divisors from a crepant resolution of singularity. The detailed structure of Coulomb branch is described as follows: a): A chamber of Coulomb branch is described by a crepant resolution, and this chamber is given by its Nef cone and the prepotential is computed from triple intersection numbers; b): Crepant resolution is not unique and different resolutions are related by flops; Nef cones from crepant resolutions form a fan which is claimed to be the full Coulomb branch.