Algebraic structure in holographic tensor networks

@misc{sahu2026algebraic,
  title = {{Algebraic structure in holographic tensor networks}},
  author = {Abhisek Sahu and Jeremy van der Heijden and Mark Van Raamsdonk and Rana Zibakhsh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00478},
  eprint = {2610.00478},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00478},
}

TY  - UNPB
TI  - Algebraic structure in holographic tensor networks
AU  - Abhisek Sahu
AU  - Jeremy van der Heijden
AU  - Mark Van Raamsdonk
AU  - Rana Zibakhsh
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.00478
UR  - https://arxiv.org/abs/2610.00478
AB  - In a previous work 2511.21852, we explored the hypothesis that in general theories of quantum gravity, spacetime regions known as generalized entanglement wedges (introduced by Bousso and Penington) have an associated subalgebra of observables in a semiclassical limit. We defined an entropy associated with these subalgebras that obeys the same monotonicity and strong subadditivity properties as the generalized gravitational entropy of generalized entanglement wedges. Here, we test aspects of these ideas making use of tensor network toy models for holography. In this context, the analog of a generalized entanglement wedge is a region for which no region containing it has a smaller number of boundary legs. In the limit of large bond dimension (analogous to the semiclassical limit), we argue that each such region has a canonically associated subalgebra of the full algebra of observables on the boundary Hilbert space, as well as a family of unitarily related von Neumann factor subalgebras. We investigate in detail how various algebraic operations on these subalgebras (e.g. their intersections, joins, and commutants) are related to corresponding geometrical operations on the tensor network regions. We study to what extent the monotonicity and strong subadditivity properties of generalized entropy for generalized entanglement wedges follow from properties of our algebraic entropy. We also introduce an alternative entropic quantity S(ω|| ω∘ E_𝒜') associated with a subalgebra 𝒜 that also obeys monotonicity and strong subadditivity properties with suitable conditions. Finally, we explain how to define a type II_1 von Neumann algebra based on an infinite family of random tensor networks with increasing bond dimension such that the regions corresponding to generalized entanglement wedges can be associated with exact subalgebras of this full algebra.
ER  -