Connecting 5d Higgs branches via Fayet-Iliopoulos deformations

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.

Automated summary

In this paper, the authors investigate the transformation of the Higgs branch geometry of 5d superconformal field theories under movement along the extended Coulomb branch. They establish a correspondence between Fayet-Iliopoulos deformations in 3d and 5d mass deformations, and utilize this correspondence to establish a local version of mirror symmetry in cases where the Higgs branch has multiple cones characterized by a collection of magnetic quivers. Several detailed examples of deformations, including decouplings and weak-coupling limits, are provided for various conformal matter theories.