Advances in Theoretical and Mathematical Physics

Volume 19 (2015)

Number 6

Singularities and gauge theory phases

Pages: 1183 – 1247



Mboyo Esole (Department of Mathematics and Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A.)

Shu-Heng Shao (Jefferson Physical Laboratory and Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Shing-Tung Yau (Harvard University, Cambridge, Massachusetts, U.S.A.; and Taida Institute for Mathematical Science, National Taiwan University, Taipei, Taiwan)


Motivated by $\mathrm{M}$-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 $\mathcal{N} = 1$ 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.

Published 5 May 2016