Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations

Understand

We describe how the geometry of the Higgs branch of 5d superconformal field theories is transformed under movement along the extended Coulomb branch.

• Working directly with the (unitary) magnetic quiver, we demonstrate a correspondence between Fayet-Iliopoulos deformations in 3d and 5d mass deformations.
• When the Higgs branch has multiple cones, characterised by a collection of magnetic quivers, the mirror map is not globally well-defined, however we are able to utilize the correspondence to establish a local version of mirror symmetry.
• We give several detailed examples of deformations, including decouplings and weak-coupling limits, in $(D_n,D_n)$ conformal matter theories, $T_N$ theory and its parent $P_N$, for which we find new Lagrangian descriptions given by quiver gauge theories with fundamental and anti-symmetric matter.