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Working in a $1/J$ expansion, we find that the large-$J$ sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge $J$ is always a scalar operator whose dimension $\\Delta_J$ satisf"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.01537","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-05-06T23:05:37Z","cross_cats_sorted":[],"title_canon_sha256":"1d5dc3c04d293c07fa38136a4b373699ce4b1a047aa1b3f2d33b7c6dd9165f30","abstract_canon_sha256":"ca30749937b7fb40bf3ade2cf929368e8f179e0c0e4ed2fe1398524058e0e08e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:23:18.997802Z","signature_b64":"yWbSo06l+xdKet+UX977vwLkjwvuyRPHUEW+G0qFrtL21wtg/yfCuTwfq4ZNaBn9MRxavHeodnb+AkKz8yy/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3126b2efb7a14df14e31e8d96cbef4d51921bf653929415df93cc9e1933d1f27","last_reissued_at":"2026-07-05T00:23:18.997294Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:23:18.997294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the CFT Operator Spectrum at Large Global Charge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Domenico Orlando, Masataka Watanabe, Simeon Hellerman, Susanne Reffert","submitted_at":"2015-05-06T23:05:37Z","abstract_excerpt":"We calculate the anomalous dimensions of operators with large global charge $J$ in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a $W = \\Phi^3$ superpotential. Working in a $1/J$ expansion, we find that the large-$J$ sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. 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