2024/01/04 by Jesse Held, Held, Jesse, Molly Kaplan +5 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2401.02487
openalex publication_date 2024/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region R and its complement R, standard RTNs are most analogous to fixed-area states of the bulk quantum gravity theory, in which quantum fluctuations have been suppressed for the area of the corresponding HRT surface. However, such RTNs have flat entanglement spectra for all choices of R, R, while quantum fluctuations of multiple HRT-areas can be suppressed only when the corresponding HRT-area operators mutually commute. We probe the severity of such obstructions in pure AdS3 Einstein-Hilbert gravity by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. Since d=3, codimension-2 extremal-surfaces are geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT surface for which all link-areas commute. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with entanglement-wedge cross sections and may be of more general interest.