The Higgs Branch of 6d (1,0) SCFTs & LSTs with DE-type SUSY Enhancement

TL;DR

This paper explores the Higgs branches of 6d (1,0) SCFTs and LSTs with supersymmetry enhancement to (2,0) theories of type DE, using geometric engineering, brane descriptions, and magnetic quivers to analyze their structure.

Contribution

It introduces a magnetic quiver approach and a slice subtraction rule to analyze Higgs branches and their foliation structure in 6d (1,0) SCFTs and LSTs with DE-type SUSY enhancement.

Findings

Magnetic quivers for Higgs branches are constructed using Type IIA brane setups.

A new 'slice subtraction' rule relates tensor branch data to Higgs branch slices.

Conjecture of transverse slices in the Higgsable to E-type (2,0) theories.

Abstract

We detail the Higgs branches of 6d $(1,0)$ superconformal field theories (SCFTs) and little string theories (LSTs) that exhibit supersymmetry-enhancing Higgs branch renormalization group flows to the 6d $(2,0)$ SCFTs and LSTs of type DE. Generically, such theories are geometrically engineered in F-theory via a configuration of $(-2)$-curves, arranged in an (affine) DE-type Dynkin diagram, and supporting special unitary gauge algebras; this describes the effective field theory on the tensor branch of the SCFT. For the Higgsable to D-type $(2,0)$ SCFTs/LSTs, there generically also exists a Type IIA brane description, involving a Neveu--Schwarz orientifold plane, which allows for the derivation of a magnetic quiver for the Higgs branch. These are 3d $\mathcal{N}=4$ unitary-orthosymplectic quivers whose Coulomb branch is isomorphic to the Higgs branch of the 6d theories. From this magnetic quiver, together with an extended quiver subtraction algorithm that we explain, the foliation structure of the Higgs branch as a symplectic singularity is unveiled. For this class of 6d SCFTs, we observe a simple rule, which we refer to as "slice subtraction," to read off the transverse slice in the foliation from the tensor branch. Based on this slice subtraction observation, we conjecture the transverse slices in the Higgsable to E-type $(2,0)$ Hasse diagram, where the SCFTs lack any known magnetic quiver for their Higgs branches.