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The Conformal Spectrum of Non-Abelian Anyons

by Nima Doroud, David Tong, Carl Turner

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Submission summary

Authors (as Contributors): Nima Doroud · David Tong · Carl Turner
Submission information
Arxiv Link: (pdf)
Date submitted: 2017-02-06 01:00
Submitted by: Tong, David
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Mathematical Physics
Approach: Theoretical


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:
Has been resubmitted

Submission & Refereeing History

Resubmission 1611.05848v2 on 7 March 2018

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Submission 1611.05848v1 on 6 February 2017

Reports on this Submission

Anonymous Report 1 on 2017-4-28 (Invited Report)


1. The authors make a clear connection with the abelian three-anyon problem
2. The introduction is well written
3. Quantum mechanical conformal invariance is well-explained
4. The authors use this invariance to determine the spectrum of non-abelian anyons
5. As an alternative, they use perturbation theory to determine the spectrum of some of the states


1. The authors should include a plot like figure 1 to illustrate the difference between abelian and non abelian anyons.
It would be nice to see which states can be calculated analytically and which ones are not.

2. It is not clear which fraction of the states are accessible analytically. Could the authors comment on that?


This is a well written paper that should be published after including the suggestions below.

Requested changes

1. Add a figure as Fig. 1 for the case of three nonabelian anyons (with only the analytical states).
2. Explain how the nonabelian action affects the number of states that can be obtained analytically.

  • validity: high
  • significance: good
  • originality: good
  • clarity: good
  • formatting: good
  • grammar: excellent

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