{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1995:PNINZOQXAPHMF25JLRXC7ESEEJ","short_pith_number":"pith:PNINZOQX","schema_version":"1.0","canonical_sha256":"7b50dcba1703cec2eba95c6e2f92442248b8d87e0792f9d28b5ff6a89948d302","source":{"kind":"arxiv","id":"hep-th/9506102","version":1},"attestation_state":"computed","paper":{"title":"Instantons and recursion relations in N=2 Susy gauge theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Marco Matone","submitted_at":"1995-06-15T17:37:12Z","abstract_excerpt":"We find the transformation properties of the prepotential ${\\cal F}$ of $N=2$ SUSY gauge theory with gauge group $SU(2)$. In particular we show that ${\\cal G}(a)=\\pi i\\left({\\cal F}(a)-{1\\over 2}a\\partial_a{\\cal F}(a)\\right)$ is modular invariant. This function satisfies the non-linear differential equation $\\left(1-{\\cal G}^2\\right){\\cal G}''+{1\\over 4}a {{\\cal G}'}^3=0$, implying that the instanton contribution are determined by recursion relations. Finally, we find $u=u(a)$ and give the explicit expression of ${\\cal F}$ as function of $u$. These results can be extended to more general cases"},"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":"hep-th/9506102","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1995-06-15T17:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"4ed9df177db64178b2164f5de6640d842b3cd853fbbdb3749b2481c36b86405a","abstract_canon_sha256":"54ca93c8211f990cb047d691aac824a073d86eb4f988e8e928b6dcfa924d2636"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:59:24.312861Z","signature_b64":"yCqJv2AHJsrDy1v0e7zCpN56nNYjBLEH45QEUSSrLeK1pYe569pKM6avc60QAbKFogeXjXF8Lnbn9CoawJc7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b50dcba1703cec2eba95c6e2f92442248b8d87e0792f9d28b5ff6a89948d302","last_reissued_at":"2026-07-04T15:59:24.312510Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:59:24.312510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Instantons and recursion relations in N=2 Susy gauge theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Marco Matone","submitted_at":"1995-06-15T17:37:12Z","abstract_excerpt":"We find the transformation properties of the prepotential ${\\cal F}$ of $N=2$ SUSY gauge theory with gauge group $SU(2)$. In particular we show that ${\\cal G}(a)=\\pi i\\left({\\cal F}(a)-{1\\over 2}a\\partial_a{\\cal F}(a)\\right)$ is modular invariant. This function satisfies the non-linear differential equation $\\left(1-{\\cal G}^2\\right){\\cal G}''+{1\\over 4}a {{\\cal G}'}^3=0$, implying that the instanton contribution are determined by recursion relations. Finally, we find $u=u(a)$ and give the explicit expression of ${\\cal F}$ as function of $u$. These results can be extended to more general cases"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9506102","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9506102/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9506102","created_at":"2026-07-04T15:59:24.312567+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9506102v1","created_at":"2026-07-04T15:59:24.312567+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9506102","created_at":"2026-07-04T15:59:24.312567+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNINZOQXAPHM","created_at":"2026-07-04T15:59:24.312567+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNINZOQXAPHMF25J","created_at":"2026-07-04T15:59:24.312567+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNINZOQX","created_at":"2026-07-04T15:59:24.312567+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2606.12529","citing_title":"Analytic approaches to perturbations of strongly coupled Yang-Mills plasma","ref_index":38,"is_internal_anchor":true},{"citing_arxiv_id":"2603.19168","citing_title":"Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization","ref_index":46,"is_internal_anchor":true},{"citing_arxiv_id":"2603.11012","citing_title":"Bouncing singularities and thermal correlators on line defects","ref_index":149,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ","json":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ.json","graph_json":"https://pith.science/api/pith-number/PNINZOQXAPHMF25JLRXC7ESEEJ/graph.json","events_json":"https://pith.science/api/pith-number/PNINZOQXAPHMF25JLRXC7ESEEJ/events.json","paper":"https://pith.science/paper/PNINZOQX"},"agent_actions":{"view_html":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ","download_json":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ.json","view_paper":"https://pith.science/paper/PNINZOQX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9506102&json=true","fetch_graph":"https://pith.science/api/pith-number/PNINZOQXAPHMF25JLRXC7ESEEJ/graph.json","fetch_events":"https://pith.science/api/pith-number/PNINZOQXAPHMF25JLRXC7ESEEJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ/action/storage_attestation","attest_author":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ/action/author_attestation","sign_citation":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ/action/citation_signature","submit_replication":"https://pith.science/pith/PNINZOQXAPHMF25JLRXC7ESEEJ/action/replication_record"}},"created_at":"2026-07-04T15:59:24.312567+00:00","updated_at":"2026-07-04T15:59:24.312567+00:00"}