Exploring the orthosymplectic zoo

TL;DR

This paper investigates the Higgs branches of 5d SO(6) and SO(8) gauge theories, comparing magnetic quivers with SU(4) theories, and explores novel phenomena in magnetic quivers including matter representations and Hilbert series calculations.

Contribution

It introduces new insights into magnetic quivers for SO(6) and SO(8) theories, including the effects of triality and novel matter configurations.

Findings

Magnetic quivers for SO(6) and SU(4) theories are contrasted.

Identifies new phenomena like hypermultiplets between symplectic nodes.

Provides a method for Coulomb branch Hilbert series with bad USp(2) nodes.

Abstract

We study the Higgs branch of the SCFT limit of 5d SO(6) and SO(8) gauge theory with hypermultiplets in the spinor and vector representations. In the case of SO(6) gauge theories, we contrast the magnetic quivers obtained with those of SU(4) gauge theory with hypermultiplets in the fundamental and second rank antisymmetric representations. Since SU(4) gauge theories admit several different values of the Chern-Simons level, we make some observations about how to distinguish those theories from the brane webs of the SO(6) theories. In the case of SO(8) gauge theories, we use SO(8) triality to propose (naively) inequivalent magnetic quivers, which will turn out to have the same moduli spaces of vacua, at least locally around their most singular loci. We encounter several interesting new phenomena occurring in the magnetic quivers, such as hypermultiplets between neighbouring symplectic gauge nodes and matter in two-index representations of unitary nodes. We also give a prescription for computing the local Coulomb branch Hilbert series for quivers involving bad USp(2) gauge nodes.