Topological pseudo entropy

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.

arXiv comment45 pages, 20 figures

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• Holography in de Sitter Space via Chern-Simons Gauge Theory
• CFT duals of three-dimensional de Sitter gravity
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• On the Page curve under final state projection
• Constructible reality condition of pseudo entropy via pseudo-Hermiticity
• SVD Entanglement Entropy
• Zoo of holographic moving mirrors
• On the real-time evolution of pseudo-entropy in 2d CFTs
• Entanglement Phase Transition in Holographic Pseudo Entropy
• Pseudo entropy under joining local quenches
• Relation between time- and spacelike entanglement entropy
• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• Sum rule for the pseudo-Rényi entropy
• Musings on SVD and pseudo entanglement entropies
• Holographic timelike entanglement in AdS${}_3$ Vaidya
• Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity
• Symmetry Properties of Quantum Dynamical Entropy
• Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
• Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas