Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations

TL;DR

This paper explores how the Higgs branch geometry of 5d superconformal theories changes under Coulomb branch movements, revealing a local mirror symmetry and new Lagrangian descriptions through magnetic quivers and FI deformations.

Contribution

It establishes a correspondence between 3d and 5d FI deformations, and introduces a local mirror symmetry framework for complex Higgs branch geometries using magnetic quivers.

Findings

Demonstrated the FI deformation correspondence in 3d and 5d.

Established local mirror symmetry for multi-cone Higgs branches.

Derived new Lagrangian quiver gauge theories for specific conformal matter theories.

Abstract

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.