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.
Highlights
A quantity called the pseudo entropy was introduced in [17], mainly motivated by finding a counterpart to a generalization of holographic entanglement entropy [18,19,20,21,22] to Euclidean time-dependent backgrounds
We 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
We find that the topological interface entropy for rational CFTs has a contribution identical to the topological entanglement entropy on a torus
Summary
Consider the three-dimensional Chern-Simons gauge theory with the gauge group SU(N ) at level k. The partition functions of the Chern-Simons theory with Wilson lines can be calculated from the knowledge of two-dimensional (2d) conformal field theory of SU(N )k Wess-Zumino-Witten (WZW) model [6] as quantum states in the Chern-Simons theory correspond to the conformal blocks of the 2d CFT. First we explain how to calculate pseudo entropy in Chern-Simons theory from section 2.1 to section 2.3. We consider the definition of boundary states in Chern-Simons theory by analogy with boundary conformal field theory (BCFT) for comparison with the results in later sections. We investigate another example of multi-boundary states in Chern-Simons theory in appendix B
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