Effective field theories for the $\nu = 5/2$ edge

TL;DR

This paper explores various effective theories, both abelian and non-abelian, that could describe the quantum Hall edge at filling fraction 5/2, comparing their predictions with experiments to identify distinguishable features.

Contribution

It introduces new candidate effective theories for the 5/2 quantum Hall edge and analyzes their experimental distinguishability.

Findings

Multiple compatible abelian and non-abelian theories identified

Quasihole tunneling data insufficient to distinguish all theories

Suggestions for additional experiments to resolve ambiguities

Abstract

We present a list of possible effective theories which may describe a QHE edge at filling fraction $\nu =5/2$. We show that there exist several abelian and non-abelian effective theories (apart from those discussed in the literature) compatible with the physical requirements imposed by the microscopic nature of the system. We compare predictions of these theories with previous proposals and with the results of recent experiments. We identify a set of theories, both abelian and non-abelian, that cannot be distinguished based on the quasihole tunneling data only. We discuss what experimental information may be useful in resolving the ambiguity.