{"paper":{"title":"Meromorphic CFTs have central charges c = 8$\\mathbb{N}$: a proof based on the MLDE approach and Rademacher series","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP","math.NT","math.QA"],"primary_cat":"hep-th","authors_text":"Arpit Das","submitted_at":"2023-12-04T18:53:51Z","abstract_excerpt":"In this short note, we present a simple and elementary proof that meromorphic conformal field theories (CFTs) have central charges of the form: $c=8N$ with $N\\in\\mathbb{N}$ (the set of natural numbers) using the modular linear differential equations (MLDEs) approach. We first set up the 1-character MLDE for arbitrary value of the Wronskian index: $\\ell$. From this we get the general form of the meromorphic CFT's character. We then study its modular transformations and the asymptotic value of it's Fourier coefficients -- using Rademacher series -- to conclude that odd values of $\\ell$ make the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.02129","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/2312.02129/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"}