The holographic dual of the entanglement wedge symplectic form

• Published in: The journal of high energy physics Vol. 2020; no. 1; pp. 71 - 36
• Main Author: Kirklin, Josh
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Bulk density; Curvature; Dictionaries; Entanglement; Gauge-gravity correspondence; Gravity; High energy physics; Hilbert space; Holography; Operators (mathematics); Quantum field theory; Regular Article - Theoretical Physics; Spacetime; Transition probabilities; Wedges; AdS-CFT Correspondence; Gauge-gravity correspondence
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2020)071

A bstract In this paper, we find the boundary dual of the symplectic form for the bulk fields in any entanglement wedge. The key ingredient is Uhlmann holonomy, which is a notion of parallel transport of purifications of density matrices based on a maximisation of transition probabilities. Using a replica trick, we compute this holonomy for curves of reduced states in boundary subregions of holographic QFTs at large N , subject to changes of operator insertions on the boundary. It is shown that the Berry phase along Uhlmann parallel paths may be written as the integral of an abelian connection whose curvature is the symplectic form of the entanglement wedge. This generalises previous work on holographic Berry curvature.