{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:STQWV2GL6UZT4QDWN2ACPX24AV","short_pith_number":"pith:STQWV2GL","schema_version":"1.0","canonical_sha256":"94e16ae8cbf5333e40766e8027df5c0567a7fdf8dfb6cb1f89e7d6ea6f1f840d","source":{"kind":"arxiv","id":"1707.03866","version":2},"attestation_state":"computed","paper":{"title":"Bosonic Tensor Models at Large $N$ and Small $\\epsilon$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Grigory Tarnopolsky, Igor R. Klebanov, Simone Giombi","submitted_at":"2017-07-12T18:52:48Z","abstract_excerpt":"We study the spectrum of the large $N$ quantum field theory of bosonic rank-$3$ tensors, whose quartic interactions are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to determine the scaling dimensions of the bilinear operators of arbitrary spin. Using the fact that the theory is renormalizable in $d=4$, we compare some of these results with the $4-\\epsilon$ expansion, finding perfect agreement. This helps elucidate why the dimension of operator $\\phi^{abc}\\phi^{abc}$ is complex for $d<4$: the large $N$ fixed point in $d=4-\\epsi"},"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":"1707.03866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-07-12T18:52:48Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"dc1900de56e901fccd7601a8beb71c2cb5caba2b8145ffd95382a3981766129c","abstract_canon_sha256":"1301bef1963a8dd3537f614a7b8ef3b03ad5c36df7d45f9d460504187f60d109"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:29.874118Z","signature_b64":"1DD8K4MmJUpK8lV3K+/vXV4DZFT8WbrRWBFLyOwUJhDa7w2D2gsdjTnRFjATv7wa7VYD54/EXXxFAvReIcOqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e16ae8cbf5333e40766e8027df5c0567a7fdf8dfb6cb1f89e7d6ea6f1f840d","last_reissued_at":"2026-05-18T00:29:29.873421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:29.873421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bosonic Tensor Models at Large $N$ and Small $\\epsilon$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Grigory Tarnopolsky, Igor R. Klebanov, Simone Giombi","submitted_at":"2017-07-12T18:52:48Z","abstract_excerpt":"We study the spectrum of the large $N$ quantum field theory of bosonic rank-$3$ tensors, whose quartic interactions are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to determine the scaling dimensions of the bilinear operators of arbitrary spin. Using the fact that the theory is renormalizable in $d=4$, we compare some of these results with the $4-\\epsilon$ expansion, finding perfect agreement. This helps elucidate why the dimension of operator $\\phi^{abc}\\phi^{abc}$ is complex for $d<4$: the large $N$ fixed point in $d=4-\\epsi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03866","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.03866","created_at":"2026-05-18T00:29:29.873511+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.03866v2","created_at":"2026-05-18T00:29:29.873511+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03866","created_at":"2026-05-18T00:29:29.873511+00:00"},{"alias_kind":"pith_short_12","alias_value":"STQWV2GL6UZT","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"STQWV2GL6UZT4QDW","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"STQWV2GL","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.19810","citing_title":"$\\phi^6$ at $6$ (and some $8$) loops in $3d$","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV","json":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV.json","graph_json":"https://pith.science/api/pith-number/STQWV2GL6UZT4QDWN2ACPX24AV/graph.json","events_json":"https://pith.science/api/pith-number/STQWV2GL6UZT4QDWN2ACPX24AV/events.json","paper":"https://pith.science/paper/STQWV2GL"},"agent_actions":{"view_html":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV","download_json":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV.json","view_paper":"https://pith.science/paper/STQWV2GL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.03866&json=true","fetch_graph":"https://pith.science/api/pith-number/STQWV2GL6UZT4QDWN2ACPX24AV/graph.json","fetch_events":"https://pith.science/api/pith-number/STQWV2GL6UZT4QDWN2ACPX24AV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV/action/storage_attestation","attest_author":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV/action/author_attestation","sign_citation":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV/action/citation_signature","submit_replication":"https://pith.science/pith/STQWV2GL6UZT4QDWN2ACPX24AV/action/replication_record"}},"created_at":"2026-05-18T00:29:29.873511+00:00","updated_at":"2026-05-18T00:29:29.873511+00:00"}