Gravity and the crossed product
By E. Witten. Journal of High Energy Physics, 2021
186 citations recorded by the source corpus.
Recently Leutheusser and Liu [1, 2] identified an emergent algebra of Type III1 in the operator algebra of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 super Yang-Mills theory for large N. Here we describe some 1/N corrections to this picture and show that the emergent Type III1 algebra becomes an algebra of Type II∞. The Type II∞ algebra is the crossed product of the Type III1 algebra by its modular automorphism group. In the context of the emergent Type II∞ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/982a204a39d99ce0b76152a47cebc66d1bbfcba7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
- Venkat Chandrasekaran
- Geoff Penington
- Roberto Longo
- E. Witten
- F. Cachazo
- Zhenbin Yang
- N. Seiberg
- L. Mason
In Nuclear and High Energy Physics
- Venkat Chandrasekaran
- Geoff Penington
- Roberto Longo
- E. Witten
- F. Cachazo
- D. Gaiotto
- Sergei Gukov
- Yuji Tachikawa
In Statistical and Nonlinear Physics
- Venkat Chandrasekaran
- Geoff Penington
- Roberto Longo
- E. Witten
- F. Cachazo
- Sergei Gukov
- Tudor Dimofte
- Yuji Tachikawa
Citations in the corpus
- Analyticity and the Unruh effect: a study of local modular flow (2024, unknown): “…flow have been used to argue that a perturbative treatment of diffeomorphism invariance in quantum gravity leads to finite renormalized entropy differences for static anti-de Sitter black holes [22–24], the static patch of de Sitter spacetime [25], and more general spacetime regions [26, 27].”
- An algebra of observables for de Sitter space (2022, methodology): “In an asymptotic expansion near N = ∞, the algebra of observables outside a black hole horizon is of Type II∞ [26].”