{"paper":{"title":"Weak Liouville quantum gravity metrics with matter central charge $\\mathbf{c} \\in (-\\infty, 25)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Joshua Pfeffer","submitted_at":"2021-04-08T19:30:53Z","abstract_excerpt":"Physics considerations suggest that a theory of Liouville quantum gravity (LQG) should exist for all values of matter central charge $\\mathbf{c} \\in (-\\infty,25)$. Probabilists have rigorously defined LQG as a random metric measure space for $\\mathbf{c} < 1$; however, they have only very recently begun to explore LQG in the $\\mathbf{c} \\in (1,25)$ phase. We define a random metric associated to LQG for all $\\mathbf{c} < 25$ by a collection of axioms analogous to axioms stated in the $\\mathbf{c} < 1$ setting. We show that such a metric exists for each $\\mathbf{c}$ by considering an approximating"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.04020","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/2104.04020/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"}