Connecting 5d Higgs branches via Fayet-Iliopoulos deformations

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 (Dn, Dn) conformal matter theories, TN theory and its parent PN, for which we find new Lagrangian descriptions given by quiver gauge theories with fundamental and anti-symmetric matter.

Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions

“…The MQ associated to a 5d SCFT is a 3d N = 4 theory whose Coulomb branch is isomorphic to the Higgs branch of the 5d SCFT. Magnetic quivers have been a very powerful tool to explore the moduli spaces of superconformal theories with 8 supercharges, with most approaches based on brane-webs [12][13][14][15][16][17][18][19][20][21][22][23][24]. From a geometric perspective, the magnetic quivers were studied e.g.…”

The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories

“…These are quivers whose Coulomb branch, when understood as a 3d theory, coincides with the Higgs branch of our 4d theory of interest (the same notion applies to 5 or 6 dimensional theories) [269][270][271][272][273][274]. 70 They can be computed from the brane construction of the theory [274][275][276][277][278][279][280][281] or from its geometric engineering [49,201,225,246,282,283], and can be used to obtain information about the Higgs branch of the theory, such as its symmetries, the stratification of the symplectic singularity, etc. [281,[284][285][286][287][288][289][290].…”

“…70 They can be computed from the brane construction of the theory [274][275][276][277][278][279][280][281] or from its geometric engineering [49,201,225,246,282,283], and can be used to obtain information about the Higgs branch of the theory, such as its symmetries, the stratification of the symplectic singularity, etc. [281,[284][285][286][287][288][289][290].…”

Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers

“…These changes are due to new massless degrees of freedom arising from tensionless strings in 6d, massless gauge instantons in 5d, and Argyres-Douglas points in 4d. Recently, magnetic quivers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] have been systematically introduced with the aim to uniformly address Higgs branches of theories with 8 supercharges in dimensions 4 to 6. For this an auxiliary quiver gauge theory Q is utilised such that its 3d N = 4 Coulomb branch C provides a geometric description of the desired Higgs branch H of a theory T in a phase P : H (T, P ) = C (Q(T, P )) .…”