Three dimensional canonical singularity and five dimensional N $$ \mathcal{N} $$ = 1 SCFT

Abstract

Abstract We conjecture that every three dimensional canonical singularity defines a five dimensional N $$ \mathcal{N} $$ = 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.

Keywords

• Extended Supersymmetry
• M-Theory
• Supersymmetry and Duality