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The Conformal Spectrum of Non-Abelian Anyons

Nima Doroud, David Tong, Carl Turner

SciPost Phys. 4, 022 (2018) · published 30 April 2018


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.

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Anyons Chern-Simons theory Conformal field theory (CFT) Harmonic traps Non-abelian statistics Quadratic Casimirs

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