{"paper":{"title":"A Hint on the External Field Problem for Matrix Models","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"L. Chekhov, Yu. Makeenko","submitted_at":"1992-02-03T17:31:00Z","abstract_excerpt":"We reexamine the external field problem for $N\\times N$ hermitian one-matrix models. We prove an equivalence of the models with the potentials $\\tr{({1/over2N}X^2 + \\log X - \\Lambda X)}$ and $\\sum_{k=1}^\\infty t_k\\tr{X^k}$ providing the matrix $\\Lambda$ is related to $\\{t_k\\}$ by $t_k=\\fr 1k \\tr{\\Lambda^{-k}}-\\frac N2 \\delta_{k2}$. Based on this equivalence we formulate a method for calculating the partition function by solving the Schwinger--Dyson equations order by order of genus expansion. Explicit calculations of the partition function and of correlators of conformal operators with the pun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9202006","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/9202006/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"}