{"paper":{"title":"Bounds on CFTs with $W_3$ algebras and AdS$_3$ higher spin theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Luis Apolo","submitted_at":"2017-05-29T21:34:48Z","abstract_excerpt":"The scaling dimension of the first excited state in two-dimensional conformal field theories (CFTs) satisfies a universal upper bound. Using the modular bootstrap, we extend this result to CFTs with $W_3$ algebras which are generically dual to higher spin theories in AdS$_3$. Assuming unitarity and modular invariance, we show that the conformal weights $h$, $\\bar{h}$ of the lightest charged state satisfy $h < c/12 + O(1)$ and $\\bar{h} < \\bar{c}/12 + O(1)$ in the limit where the central charges $c$, $\\bar{c}$ are large. Furthermore, we show that in this limit any consistent CFT with $W_3$ curre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10402","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":""},"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"}