Abstract
We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work [35].
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Wen, X., Chang, PY. & Ryu, S. Topological entanglement negativity in Chern-Simons theories. J. High Energ. Phys. 2016, 12 (2016). https://doi.org/10.1007/JHEP09(2016)012
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DOI: https://doi.org/10.1007/JHEP09(2016)012