{"paper":{"title":"The c-d conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Germ\\'an Sierra, Jos\\'e I. Latorre","submitted_at":"2024-03-25T22:44:15Z","abstract_excerpt":"We conjecture a relation between the local dimension $d$ of a local nearest-neighbor critical Hamiltonian in one spatial dimension and the maximum central charge, $c_{\\text{max}}$, that it can yield. Specifically, we propose that $c_{\\text{max}} \\leq d-1$, establishing a link between the short-distance lattice realization of a model and its emerging long-distance entanglement properties. This inequality can be viewed as a general form of a $c$-theorem establishing the reduction of effective degrees of freedom between the UV lattice and the IR conformal field theory. We support this conjecture "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17242","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/2403.17242/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"}