On the torus compactifications of Z ₂ orbifolds of E-string theories

We consider the torus compactifications with flux of a class of 6d (1, 0) SCFTs that can be engineered as the low-energy theories on M5-branes near an M9-plane on a C² / Z₂ singularity. Specifically, we concentrate on the two SCFTs where the Z₂ orbifold action acts non-trivially on the E₈ global symmetry. We analyze this problem by compactifying to 5d, where we can exploit the relation to 5d duality domain walls. By a suitable guess of the domain wall theories, the resulting 4d theories can be conjectured. These can then be tested by comparing their properties, notably anomalies and symmetries, against the 6d expectations. These constructions lead to various interesting 4d phenomena like dualities and symmetry enhancements.