Large $N$ von Neumann algebras and the renormalization of Newton's constant

• URL: http://arxiv.org/abs/2302.01938v2
• Date: Fri, 28 Jul 2023 01:28:55 GMT
• Title: Large $N$ von Neumann algebras and the renormalization of Newton's constant
• Authors: Elliott Gesteau
• Abstract summary: I derive a family of Ryu--Takayanagi formulae valid in the large $N$ limit of holographic quantum error-correcting codes. I show that the renormalizations of the area term and the bulk entropy term exactly compensate each other.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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