Coulomb and Higgs Branches from Canonical Singularities: Part 0

Understand

Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively.

• We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities.
• We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d $\mathcal{N}=4$ mirror symmetry and an $S$-type gauging of an abelian flavor symmetry.
• In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry.