{"paper":{"title":"Reflected entropy in random tensor networks II: a topological index from the canonical purification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Chris Akers, Pratik Rath, Simon Lin, Thomas Faulkner","submitted_at":"2022-10-26T20:03:29Z","abstract_excerpt":"In arXiv:2112.09122, we analyzed the reflected entropy ($S_R$) in random tensor networks motivated by its proposed duality to the entanglement wedge cross section (EW) in holographic theories, $S_R=2 \\frac{EW}{4G}$. In this paper, we discover further details of this duality by analyzing a simple network consisting of a chain of two random tensors. This setup models a multiboundary wormhole. We show that the reflected entanglement spectrum is controlled by representation theory of the Temperley-Lieb (TL) algebra. In the semiclassical limit motivated by holography, the spectrum takes the form of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15006","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.15006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}