## SciPost Submission Page

# The Conformal Spectrum of Non-Abelian Anyons

### by Nima Doroud, David Tong, Carl Turner

#### - Published as SciPost Phys. 4, 022 (2018)

### Submission summary

As Contributors: | Nima Doroud · David Tong |

Arxiv Link: | https://arxiv.org/abs/1611.05848v2 |

Date accepted: | 2018-03-19 |

Date submitted: | 2018-03-07 |

Submitted by: | Tong, David |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Mathematical Physics |

### Abstract

We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents.

###### Current status:

### Ontology / Topics

See full Ontology or Topics database.### Author comments upon resubmission

The referee raises an interesting question: what fraction of the states in the system are under analytic control? Unfortunately this appears to be a rather difficult problem and we do not have the general solution. Indeed, even for seemingly simple cases, like 3 anyons in SU(2), it is complicated.

In an attempt to improve the paper along the lines suggested by the referee, we have included a plot of the low lying states of two SU(2) anyons, in which we include both analytic and non-analytic states. We have elaborated on the difficulty in counting the analytic states in general.

### List of changes

The changes are all on page 21. The referee requested a plot of analytic states for 3 anyons to match that in the introduction. While this plot is simple to construct, we felt that it didn't add much without knowing the non-analytic states as well. This is why we plumped for two anyons instead.