Large N von Neumann Algebras and the Renormalization of Newton's Constant
Abstract
I derive a family of Ryu–Takayanagi formulae that are valid in the large N limit of holographic quantum error-correcting codes, and parameterized by a choice of UV cutoff in the bulk. The bulk entropy terms are matched with a family of von Neumann factors nested inside the large N von Neumann algebra describing the bulk effective field theory. These factors are mapped onto one another by a family of conditional expectations, which are interpreted as a renormalization group flow for the code subspace. Under this flow, I show that the renormalizations of the area term and the bulk entropy term exactly compensate each other. This result provides a concrete realization of the ER=EPR paradigm, as well as an explicit proof of a conjecture due to Susskind and Uglum.
Copyright and License
This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection
may apply 2024.
Acknowledgement
I am grateful to Chris Akers, Juan Felipe Ariza Mejia, Adam Artymowicz, Charles Cao, Tom Faulkner, Alex Jahn, Matilde Marcolli, Daniel Murphy, Geoff Penington, Leonardo Santilli and David Simmons-Duffin for discussions and correspondence. I would also like to thank Chris Akers, Tom Faulkner, Matilde Marcolli and Daniel Murphy for comments on a draft of this paper.
Data Availability
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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Related works
- Describes
- Journal Article: https://rdcu.be/d634s (URL)
- Is new version of
- Discussion Paper: arXiv:2302.01938 (arXiv)
Dates
- Accepted
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2024-11-08Accepted
- Available
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2025-01-16Published online
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- Published