Atomic Higgsings of 6D SCFTs II: Induced Flows

TL;DR

This paper investigates a specific class of Higgsing processes called induced flows in 6d $ ext{(1,0)}$ theories, analyzing their effects on Higgs branch dimensions, anomalies, and brane configurations, with a focus on conformal matter and orbifold theories.

Contribution

It introduces a physical framework for induced flows in 6d theories, connecting nilpotent orbit inductions with homomorphisms from discrete subgroups of SU(2) to E8, and analyzes their impact on various physical properties.

Findings

Higgs branch dimensions are affected predictably by induced flows.

Monotonicity of Weyl anomalies is observed under these flows.

Brane configurations evolve consistently with the induced flows.

Abstract

We study a specific type of atomic Higgsings of the 6d $\mathcal{N}=(1,0)$ theories, which we call the induced flows. For the conformal matter theory associated with a pair of nilpotent orbits, the induced flows are given by the inductions of the orbits. We also consider the induced flows for the orbi-instanton theories (as well as some little string theories) that are associated with the homomorphisms from the discrete subgroups of $\mathrm{SU}(2)$ to $E_8$. This gives a physical definition of the inductions among these discrete homomorphisms, analogous to the inductions of the nilpotent orbits. We analyze the Higgs branch dimensions, the monotonicity of the Weyl anomalies (or the 2-group structure constants for LSTs) and the brane pictures under the induced flows.