{"paper":{"title":"Constructive Renormalization of the $2$-dimensional Grosse-Wulkenhaar Model","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["hep-th","math.MP","math.OA","math.PR"],"primary_cat":"math-ph","authors_text":"Zhituo Wang","submitted_at":"2018-05-16T15:19:35Z","abstract_excerpt":"We study a quartic matrix model with partition function $Z=\\int d\\ M\\exp{\\rm Tr}\\ (-\\Delta M^2-\\frac{\\lambda}{4}M^4)$. The integral is over the space of Hermitian $(\\Lambda+1)\\times(\\Lambda+1)$ matrices, the matrix $\\Delta$, which is not a multiple of the identity matrix, encodes the dynamics and $\\lambda>0$ is a scalar coupling constant. We proved that the logarithm of the partition function is the Borel sum of the perturbation series, hence is a well defined analytic function of the coupling constant in certain analytic domain of $\\lambda$, by using the multi-scale loop vertex expansions. Al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06365","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"}