Microscopic analysis of protected edges without symmetry

The $\nu = 2/3$ fractional quantum Hall state has been shown to have protected gapless edge modes even if all symmetries are broken, including charge conservation. In this talk, we investigate the robustness of these edge modes in a concrete model. The model we consider describes a 2/3 edge that is strongly proximity-coupled to an adjacent superconductor. Our model clarifies the obstruction to gapping the edge and provides insights into the corresponding anomaly --- which is beyond the U(1) chiral anomaly associated with charge conservation symmetry. As a by-product of this analysis, we derive edge theories for Abelian quantum Hall states without any U(1) symmetries.