{"paper":{"title":"${\\cal N}=1$ Theories and a Geometric Master Field","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Allahabad), Rajesh Gopakumar (Harish-Chandra Research Institute","submitted_at":"2002-11-12T09:10:47Z","abstract_excerpt":"We study the large $N$ limit of the class of U(N) ${\\CN}=1$ SUSY gauge theories with an adjoint scalar and a superpotential $W(\\P)$. In each of the vacua of the quantum theory, the expectation values $\\la$Tr$\\Phi^p$$\\ra$ are determined by a master matrix $\\Phi_0$ with eigenvalue distribution $\\rho_{GT}(\\l)$. $\\rho_{GT}(\\l)$ is quite distinct from the eigenvalue distribution $\\rho_{MM}(\\l)$ of the corresponding large $N$ matrix model proposed by Dijkgraaf and Vafa. Nevertheless, it has a simple form on the auxiliary Riemann surface of the matrix model. Thus the underlying geometry of the matrix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0211100","kind":"arxiv","version":3},"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/0211100/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"}