Topological pseudo entropy

• Published in: The journal of high energy physics Vol. 2021; no. 9; pp. 1 - 44
• Main Authors: Nishioka, Tatsuma, Takayanagi, Tadashi, Taki, Yusuke
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer Nature B.V; SpringerOpen
• Subjects: Chern-Simons Theories; Classical and Quantum Gravitation; Conformal Field Theory; Elementary Particles; Entanglement; Entropy; Equivalence; Gauge theory; High energy physics; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Topological Field Theories; Topology; Toruses; Chern-Simons Theories; Topological Field Theories; Conformal Field Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2021)015

A bstract 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.