Atomic Higgsings of 6D SCFTs II: Induced Flows

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.