Hierarchies of RG flows in 6d $(1,0)$ massive E-strings

TL;DR

This paper classifies 6d (1,0) massive E-string theories using constrained E8 Kac labels and constructs hierarchies of RG flows between these theories, including novel flows triggered by T-brane vevs.

Contribution

It extends the classification of massive E-string theories and constructs hierarchies of Higgs branch RG flows, including new flows involving different $n_0$ parameters and T-brane vevs.

Findings

Classified massive E-string theories via constrained E8 Kac labels.

Constructed hierarchies of RG flows between theories with same and different $n_0$.

Identified novel RG flows triggered by T-brane vevs.

Abstract

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.