Abstract
We study the Seberg-Witten geometry of 5d mathcal{N} = 1 pure Yang-Mills theories compactified on a circle. The concept of the holonomy saddle implies that there are multiple 4d limits of interacting Seiberg-Witten theories from a single 5d theory, and we explore this in the simplest case of pure SU(N) theories. The compactification leads to N copies of locally indistinguishable 4d pure SU(N) Seiberg-Witten theories in the infrared, glued together in a manner dictated by the Chern-Simons level. We show how this picture naturally builds the 5d BPS quivers which agree with the D0 probe dynamics previously proposed via the geometrically engineered local Calabi-Yau. We work out various SU(2) and SU(3) examples through a detailed look at the respective spectral curves. We also note a special ℤ2N feature of SU(N)N spectral curves and the resulting BPS quivers, with emphasis on how the 4d holonomy saddles are affected.
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