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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Lee, Y., Tachikawa, Y. A study of time reversal symmetry of abelian anyons. J. High Energ. Phys. 2018, 90 (2018). https://doi.org/10.1007/JHEP07(2018)090
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DOI: https://doi.org/10.1007/JHEP07(2018)090