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Title: Crossing Versus Locking: Bit Threads and Continuum Multiflows

Abstract

Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu–Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. Here, we investigate for which choices of bound a given set of boundary regions can be “locked”, in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.

Authors:
ORCiD logo [1];  [2];  [3]
+ Show Author Affiliations
  1. Brandeis Univ., Waltham, MA (United States)
  2. Brandeis Univ., Waltham, MA (United States); Univ. of California, Santa Barbara, CA (United States)
  3. Brandeis Univ., Waltham, MA (United States); Univ. of California, Los Angeles, CA (United States)
Publication Date:
Research Org.:
Brandeis Univ., Waltham, MA (United States)
Sponsoring Org.:
Simons Foundation; USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1905191
Grant/Contract Number:  
SC0020194; SC0009987; NSF PHY-1748958
Resource Type:
Accepted Manuscript
Journal Name:
Communications in Mathematical Physics
Additional Journal Information:
Journal Volume: 396; Journal Issue: 1; Journal ID: ISSN 0010-3616
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Headrick, Matthew, Held, Jesse, and Herman, Joel. Crossing Versus Locking: Bit Threads and Continuum Multiflows. United States: N. p., 2022. Web. doi:10.1007/s00220-022-04476-w.
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Headrick, Matthew, Held, Jesse, & Herman, Joel. Crossing Versus Locking: Bit Threads and Continuum Multiflows. United States. https://doi.org/10.1007/s00220-022-04476-w
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Headrick, Matthew, Held, Jesse, and Herman, Joel. Sat . "Crossing Versus Locking: Bit Threads and Continuum Multiflows". United States. https://doi.org/10.1007/s00220-022-04476-w. https://www.osti.gov/servlets/purl/1905191.
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@article{osti_1905191,
title = {Crossing Versus Locking: Bit Threads and Continuum Multiflows},
author = {Headrick, Matthew and Held, Jesse and Herman, Joel},
abstractNote = {Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu–Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. Here, we investigate for which choices of bound a given set of boundary regions can be “locked”, in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.},
doi = {10.1007/s00220-022-04476-w},
journal = {Communications in Mathematical Physics},
number = 1,
volume = 396,
place = {United States},
year = {Sat Sep 10 00:00:00 EDT 2022},
month = {Sat Sep 10 00:00:00 EDT 2022}
}
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https://doi.org/10.1007/s00220-022-04476-w
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