  We extend the analysis of arXiv:2208.11703 to the 6d $(1,0)$ SCFTs known as
massive E-string theories, which can be engineered in massive Type IIA with
$8-n_0<8$ D8-branes close to an O8$^-$ (or O8$^*$ if $n_0=8,9$). For each
choice of $n_0=1,\ldots,9$ the massive $E_{1+(8-n_0)}$-strings (including the
more exotic $\tilde{E}_1$ and $E_0$) are classified by constrained $E_8$ Kac
labels, i.e. a subset of $\text{Hom}(\mathbb{Z}_k,E_8)$, from which one can
read off the flavor subalgebra of $E_{1+(8-n_0)}$ of each SCFT. We construct
hierarchies for two types of Higgs branch RG flows: flows between massive
theories defined by the same $n_0$ but different labels; flows between massive
theories with different $n_0$. These latter flows are triggered by T-brane
vev's for the right $\mathrm{SU}$ factor of the SCFT global symmetry, whose
rank is a function of both $k$ and $n_0$, a situation which has so far remained
vastly unexplored.

High Energy Physics - Theory