Topological pseudo entropy
- URL: http://arxiv.org/abs/2107.01797v2
- Date: Sun, 22 Aug 2021 06:56:14 GMT
- Title: Topological pseudo entropy
- Authors: Tatsuma Nishioka, Tadashi Takayanagi, Yusuke Taki
- Abstract summary: We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy.
We show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional conformal field theories.
We derive a universal formula for a pair of arbitrary boundary states.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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 (R\'enyi) 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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