The role of U(1)'s in 5d theories, Higgs branches, and geometry

Understand

We explore the Higgs branches of five-dimensional $\mathcal{N}=1$ quiver gauge theories at finite coupling from the paradigm of M-theory on local Calabi-Yau threefolds described as $\mathbb{C}^\ast$-fibrations over local K3's.

• By properly counting local deformations of singularities, we find results compatible with unitary as opposed to special unitary gauge groups.
• We interpret these results by dualizing to both IIA on local K3's with D6-branes, and to IIB with 5-branes.
• Finally, we find that, by compactifying the $\mathbb{C}^\ast$-fibers to tori, a well-known St\"uckelberg mechanism eliminates Abelian factors, and provides missing Higgs branch moduli in a very interesting way.