Topological pseudo entropy

TL;DR

This paper introduces topological pseudo entropy, extending topological entanglement entropy, and explores its properties in Chern-Simons theories and conformal field theories, revealing new connections and universal formulas.

Contribution

It defines topological pseudo entropy, relates it to Wilson loop partition functions, and establishes its equivalence to interface entropy in CFTs, providing new computational tools.

Findings

Topological pseudo entropy generalizes topological entanglement entropy.

Partition functions with knotted Wilson loops relate to pseudo entropy.

Universal formula for boundary state pairs in boundary CFTs.

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.