Atomic Higgsings of 6D SCFTs

TL;DR

This paper develops a comprehensive, geometry-based method to determine the Higgs branch Hasse diagrams of 6d $ abla$=(1,0) SCFTs, including new cases without magnetic quiver descriptions, advancing understanding of their RG flows.

Contribution

Introduces the atomic Higgsing procedure for systematically constructing Higgs branch Hasse diagrams of 6d SCFTs using F-theory, applicable to cases beyond magnetic quiver methods.

Findings

Algorithm successfully reproduces known Hasse diagrams from magnetic quivers.

Constructs orthosymplectic magnetic quivers from Type IIA brane systems.

Extends analysis to theories without magnetic quiver descriptions.

Abstract

In this paper, we study the full Higgs branch Hasse diagram for any given 6d $\mathcal{N}=(1,0)$ SCFT constructed via F-theory. This can be done by a procedure of determining all the minimal Higgsings on the generalized quiver of the 6d SCFT. We call this procedure the atomic Higgsing, which can be implemented iteratively. We present our general algorithms with many concrete examples of Hasse diagrams. We also compare our algorithm with the Higgsings determined by the 3d $\mathcal{N} = 4$ magnetic quivers. For the cases where the magnetic quivers are unitary, we can reproduce the full Hasse diagrams. We also construct the orthosymplectic magnetic quivers from the Type IIA brane systems for some new examples. Our approach, based on F-theory, applies to the known and new orthosymplectic cases, as well as theories that do not have known descriptions in terms of magnetic quivers. We expect our geometry-based approach to help extend the horizon of the RG flows of the 6d SCFTs.