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A study of time reversal symmetry of abelian anyons

  • Yasunori Lee
  • Yuji Tachikawa
Open Access
Regular Article - Theoretical Physics

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 \( \mathcal{A}={\left({\mathrm{\mathbb{Z}}}_2\right)}^N \).

Keywords

Anomalies in Field and String Theories Anyons Discrete Symmetries Topological Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Kavli Institute for the Physics and Mathematics of the UniverseUniversity of TokyoKashiwaJapan

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