Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 4

Singularities and gauge theory phases, II

Pages: 683 – 749



Mboyo Esole (Department of Mathematics, Northeastern University, Boston, Massachusetts, U.S.A.)

Shu-Heng Shao (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


We present a simple algebraic construction for all the small resolutions of the $SU(5)$ Weierstrass model. Each resolution corresponds to a subchamber on the Coulomb branch of the five-dimensional $\mathcal{N} = 1 \, SU(5)$ gauge theory with matter fields in the fundamental and two-index antisymmetric representations. This construction unifies all previous resolutions found in the literature in a single framework.

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Published 4 November 2016