Abstract
We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop insertions. Partition functions with knotted Wilson loops are directly related to topological pseudo (Rényi) entropies. We also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional conformal field theories (CFTs), and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, we define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states. As a byproduct, we find that the topological interface entropy for rational CFTs has a contribution identical to the topological entanglement entropy on a torus.
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Nishioka, T., Takayanagi, T. & Taki, Y. Topological pseudo entropy. J. High Energ. Phys. 2021, 15 (2021). https://doi.org/10.1007/JHEP09(2021)015
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DOI: https://doi.org/10.1007/JHEP09(2021)015