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arXiv · 2509.05413

The Making of von Neumann Algebras from Bulk Focusing

Netta Engelhardt·Hong Liu
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Abstract

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.

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Netta Engelhardt, Hong Liu. 2025-09-05. The Making of von Neumann Algebras from Bulk Focusing. https://arxiv.org/abs/2509.05413

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