{"paper":{"title":"The Topological CP^1 Model and the Large-N Matrix Integral","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"S.-K. Yang, T. Eguchi","submitted_at":"1994-07-21T00:54:46Z","abstract_excerpt":"We discuss the topological $CP^1$ model which consists of the holomorphic maps from Riemann surfaces onto $CP^1$. We construct a large-$N$ matrix model which reproduces precisely the partition function of the $CP^1$ model at all genera of Riemann surfaces. The action of our matrix model has the form ${\\rm Tr}\\, V(M)=-2{\\rm Tr}\\, M(\\log M -1) +2\\sum t_{n,P}{\\rm Tr}\\, M^n(\\log M-c_n) +\\sum 1/n\\cdot t_{n-1,Q}{\\rm Tr}\\, M^n~(c_n=\\sum_1^n 1/j )$ where $M$ is an $N\\times N$ hermitian matrix and $t_{n,P}\\, (t_{n,Q}),~(n=0,1,2,\\cdots)$ are the coupling constants of the $n$-th descendant of the punctur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9407134","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"}