Large $N$ von Neumann algebras and the renormalization of Newton's constant
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910788594171904 |
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| author | Gesteau, Elliott |
| author_facet | Gesteau, Elliott |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large $N$ von Neumann algebras and the renormalization of Newton's constant Gesteau, Elliott High Energy Physics - Theory Mathematical Physics Operator Algebras Quantum Physics 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. |
| title | Large $N$ von Neumann algebras and the renormalization of Newton's constant |
| topic | High Energy Physics - Theory Mathematical Physics Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2302.01938 |