{"paper":{"title":"On the large $D$ expansion of Hermitian multi-matrix models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Adrian Tanasa, Frank Ferrari, Guillaume Valette, Sylvain Carrozza","submitted_at":"2020-03-09T13:52:29Z","abstract_excerpt":"We investigate the existence and properties of a double asymptotic expansion in $1/N^{2}$ and $1/\\sqrt{D}$ in $\\mathrm{U}(N)\\times\\mathrm{O}(D)$ invariant Hermitian multi-matrix models, where the $N\\times N$ matrices transform in the vector representation of $\\mathrm{O}(D)$. The crucial point is to prove the existence of an upper bound $\\eta(h)$ on the maximum power $D^{1+\\eta(h)}$ of $D$ that can appear for the contribution at a given order $N^{2-2h}$ in the large $N$ expansion. We conjecture that $\\eta(h)=h$ in a large class of models. In the case of traceless Hermitian matrices with the qua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.04152","kind":"arxiv","version":2},"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/2003.04152/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"}