Singularities and Gauge Theory Phases

Understand

Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we present a correspondence between networks of small resolutions for singular elliptic fibrations and Coulomb branches of five-dimensional N=1 gauge theories.

• While resolutions correspond to subchambers of the Coulomb branch, partial resolutions correspond to higher codimension loci at which the Coulomb branch intersects the Coulomb-Higgs branches.
• Flops between different resolutions are identified with reflections on the Coulomb branch.
• Physics aside, this correspondence provides an interesting link between elliptic fibrations and representation theory.