Covariant bit threads

• Published in: The journal of high energy physics Vol. 2023; no. 7; pp. 180 - 90
• Main Authors: Headrick, Matthew, Hubeny, Veronika E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 24.07.2023; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: AdS-CFT Correspondence; ASTRONOMY AND ASTROPHYSICS; Black Holes; Classical and Quantum Gravitation; Diferential and Algebraic Geometry; Differential and Algebraic Geometry; Elementary Particles; Entanglement; Entropy; High energy physics; Hyperspaces; Lower bounds; Minimax technique; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spacetime; String Theory; Upper bounds; AdS-CFT Correspondence; Black Holes; Differential and Algebraic Geometry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2023)180

A bstract We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D ( A ) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D ( A ) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize the flux over a bulk Cauchy slice of a divergenceless timelike 1-form U subject to a lower bound on its norm that is non-local in space. The two flow formulas define convex programs and are related to each other by Lagrange duality. For each program, the optimal configurations dynamically find the HRT surface and the entanglement wedges of A and its complement. The V-flow formula is the covariant version of the Freedman-Headrick bit thread reformulation of the Ryu-Takayanagi formula. We also introduce a measure-theoretic concept of a “thread distribution”, and explain how Riemannian flows, V-flows, and U-flows can be expressed in terms of thread distributions.