# A study of time reversal symmetry of abelian anyons

Journal of High Energy Physics, Jul 2018

Abstract We perform a study of time reversal symmetry of abelian anyons $$\mathcal{A}$$ in 2+1 dimensions, in the spin structure independent cases. We will find the importance of the group $$\mathcal{C}$$ of time-reversal-symmetric anyons modulo anyons composed from an anyon and its time reversal. Possible choices of local Kramers degeneracy are given by quadratic refinements of the braiding phases of $$\mathcal{C}$$, and the anomaly is then given by the Arf invariant of the chosen quadratic refinement. We also give a concrete study of the cases when |$$\mathcal{A}$$| is odd or $$\mathcal{A}={\left({\mathrm{\mathbb{Z}}}_2\right)}^N$$.

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Yasunori Lee, Yuji Tachikawa. A study of time reversal symmetry of abelian anyons, Journal of High Energy Physics, 2018, 90, DOI: 10.1007/JHEP07(2018)090