{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:KJMUSS5QTOINYIEK2AXKCTJGRT","short_pith_number":"pith:KJMUSS5Q","schema_version":"1.0","canonical_sha256":"5259494bb09b90dc208ad02ea14d268cf2718ca55b71820fb1ef5e00560e2586","source":{"kind":"arxiv","id":"0908.4409","version":1},"attestation_state":"computed","paper":{"title":"On Crossing Symmmetry and Modular Invariance in Conformal Field Theory and S Duality in Gauge Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dan Xie, Dimitri Nanopoulos","submitted_at":"2009-08-30T18:16:33Z","abstract_excerpt":"In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with four fundamentals can be derived from the crossing symmetry of the Liouville four point function. We also show that the partition function of N=4 SU(2) gauge theory can be derived from the Liouville partition function on torus."},"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":"0908.4409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-08-30T18:16:33Z","cross_cats_sorted":[],"title_canon_sha256":"94b404f3f4bd14a7ff7fe642b67e5686de7ab7ca56a05abcd3dfa74c9f050636","abstract_canon_sha256":"87ef0675c51c33055c2174d46db3f92a54ec5802d05b7ec0b1d4ad24c87ad8cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:57.954848Z","signature_b64":"LAYtd9eCOE8HVAj8SyFx3VOld7bhVuaif43TDsO1lVJaNUBUv4mdCYjCuGcmbgzHAyJl+1DQvHweD0L9V5q5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5259494bb09b90dc208ad02ea14d268cf2718ca55b71820fb1ef5e00560e2586","last_reissued_at":"2026-05-18T03:23:57.954308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:57.954308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Crossing Symmmetry and Modular Invariance in Conformal Field Theory and S Duality in Gauge Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dan Xie, Dimitri Nanopoulos","submitted_at":"2009-08-30T18:16:33Z","abstract_excerpt":"In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with four fundamentals can be derived from the crossing symmetry of the Liouville four point function. We also show that the partition function of N=4 SU(2) gauge theory can be derived from the Liouville partition function on torus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4409","kind":"arxiv","version":1},"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":"0908.4409","created_at":"2026-05-18T03:23:57.954406+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.4409v1","created_at":"2026-05-18T03:23:57.954406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4409","created_at":"2026-05-18T03:23:57.954406+00:00"},{"alias_kind":"pith_short_12","alias_value":"KJMUSS5QTOIN","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"KJMUSS5QTOINYIEK","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"KJMUSS5Q","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT","json":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT.json","graph_json":"https://pith.science/api/pith-number/KJMUSS5QTOINYIEK2AXKCTJGRT/graph.json","events_json":"https://pith.science/api/pith-number/KJMUSS5QTOINYIEK2AXKCTJGRT/events.json","paper":"https://pith.science/paper/KJMUSS5Q"},"agent_actions":{"view_html":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT","download_json":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT.json","view_paper":"https://pith.science/paper/KJMUSS5Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.4409&json=true","fetch_graph":"https://pith.science/api/pith-number/KJMUSS5QTOINYIEK2AXKCTJGRT/graph.json","fetch_events":"https://pith.science/api/pith-number/KJMUSS5QTOINYIEK2AXKCTJGRT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT/action/storage_attestation","attest_author":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT/action/author_attestation","sign_citation":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT/action/citation_signature","submit_replication":"https://pith.science/pith/KJMUSS5QTOINYIEK2AXKCTJGRT/action/replication_record"}},"created_at":"2026-05-18T03:23:57.954406+00:00","updated_at":"2026-05-18T03:23:57.954406+00:00"}