Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.05413 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909773961625600 |
|---|---|
| author | Engelhardt, Netta Liu, Hong |
| author_facet | Engelhardt, Netta Liu, Hong |
| contents | The single-trace, infinite-N algebra of an arbitrary region may or may not be a von Neumann algebra depending on the GNS sector. In this paper we identify the holographic dual of this mechanism as a consequence of the focusing of null geodesics; more precisely, this GNS sector-dependence corresponds to the well-known difference between null congruences fired from the bulk and those fired from the boundary. As part of establishing this property, we give a rigorous formulation and proof of causal wedge reconstruction for those general boundary subregions whose single trace algebras support von Neumann algebras at large-N. We discuss a possible finite-N extension and interpretation of our results as an explanation for the Hawking area theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Making of von Neumann Algebras from Bulk Focusing Engelhardt, Netta Liu, Hong High Energy Physics - Theory General Relativity and Quantum Cosmology The single-trace, infinite-N algebra of an arbitrary region may or may not be a von Neumann algebra depending on the GNS sector. In this paper we identify the holographic dual of this mechanism as a consequence of the focusing of null geodesics; more precisely, this GNS sector-dependence corresponds to the well-known difference between null congruences fired from the bulk and those fired from the boundary. As part of establishing this property, we give a rigorous formulation and proof of causal wedge reconstruction for those general boundary subregions whose single trace algebras support von Neumann algebras at large-N. We discuss a possible finite-N extension and interpretation of our results as an explanation for the Hawking area theorem. |
| title | The Making of von Neumann Algebras from Bulk Focusing |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2509.05413 |