{"paper":{"title":"Cutting $\\gamma$-Liouville quantum gravity by Schramm-Loewner evolution for $\\kappa \\not\\in \\{\\gamma^2, 16/\\gamma^2\\}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Morris Ang","submitted_at":"2023-10-17T17:59:54Z","abstract_excerpt":"There are many deep and useful theorems relating Schramm-Loewner evolution (SLE$_\\kappa$) and Liouville quantum gravity ($\\gamma$-LQG) in the case when the parameters satisfy $\\kappa \\in \\{\\gamma^2, 16/\\gamma^2\\}$. Roughly speaking, these theorems say that the SLE$_\\kappa$ curve cuts the $\\gamma$-LQG surface into two or more independent $\\gamma$-LQG surfaces. We extend these theorems to the case when $\\kappa \\not\\in \\{\\gamma^2, 16/\\gamma^2\\}$. Roughly speaking we show that if we have an appropriate variant of SLE$_\\kappa$ and an independent $\\gamma$-LQG disk, then the SLE curve cuts the LQG di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.11455","kind":"arxiv","version":3},"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/2310.11455/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"}