On the torus compactifications of $Z_2$ orbifolds of E-string theories

TL;DR

This paper studies torus compactifications of specific 6d SCFTs related to M5-branes and M9-planes, revealing new 4d dualities and symmetry enhancements through anomaly and symmetry analysis.

Contribution

It introduces a novel approach to derive 4d theories from 6d SCFTs with non-trivial $Z_2$ orbifold actions using 5d duality domain walls and conjectured 4d theories.

Findings

Identification of 4d theories with specific anomaly structures

Discovery of dualities and symmetry enhancements in 4d

Validation of conjectured theories through anomaly matching

Abstract

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 M$5$-branes near an M$9$-plane on a $C^2/Z_2$ singularity. Specifically, we concentrate on the two SCFTs where the $Z_2$ orbifold action acts non-trivially on the $E_8$ 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.