Gravity and the Crossed Product

2021/12/23 by Edward Witten · 1 voice · 3 citations
Physics and Astronomy · #hep-th #gr-qc

paper · pdf · doi:10.1007/jhep10(2022)008

arxiv published 2021/12/23 · arxiv updated 2022/09/19

Abstract

Recently Leutheusser and Liu [1,2] identified an emergent algebra of Type III₁ in the operator algebra of \mathcal N=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.

Cited by

• Boundary mutual information in double holography
• A Nonperturbative Toolkit for Quantum Gravity
• Out of the box approach to Black hole Information paradox

Discussions

• Why is this exciting? Because in 2021, Witten showed that type II algebras emerge in holography from gravitational (1/N) effects. This suggests that the entanglement in holographic codes describes asp [bsky, 0 points, 1 comments]

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• The Crossed Product, Modular (Tomita) Dynamics and its Role in the Transition of Type III to Type II_∞ v.Neumann Algebras and Connections to Quantum Gravity
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• Principle of Diminishing Potentialities in Large N Algebras
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