{"paper":{"title":"The CFT of SLE loop measures and the Kontsevich--Suhov conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP","math.RT"],"primary_cat":"math.PR","authors_text":"Antoine Jego, Guillaume Baverez","submitted_at":"2024-07-12T08:09:51Z","abstract_excerpt":"This paper initiates the study of the conformal field theory of the SLE$_\\kappa$ loop measure $\\nu$ for $\\kappa\\in(0,4]$, the range where the loop is almost surely simple. First, we construct two commuting representations $(\\mathbf{L}_n,\\bar{\\mathbf{L}}_n)_{n\\in\\mathbb{Z}}$ of the Virasoro algebra with central charge $c_\\mathrm{M}=1-6(\\frac{2}{\\sqrt{\\kappa}}-\\frac{\\sqrt{\\kappa}}{2})^2\\leq1$ as (unbounded) first order differential operators on $L^2(\\nu)$. Second, we introduce highest-weight representations and characterise their structure: in particular, we prove the existence of vanishing sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.09080","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/2407.09080/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"}