{"paper":{"title":"Seeing asymptotic freedom in an exact correlator of a large-$N$ matrix field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-lat","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Peter Orland","submitted_at":"2014-10-09T21:08:49Z","abstract_excerpt":"Exact expressions for correlation functions are known for the large-$N$ (planar) limit of the $(1+1)$-dimensional ${\\rm SU}(N)\\times {\\rm SU}(N)$ principal chiral sigma model. These were obtained with the form-factor bootstrap, an entirely nonperturbative method. The large-$N$ solution of this asymptotically-free model is far less trivial than that of O($N$) sigma model (or other isovector models). Here we study the Euclidean two-point correlation function $N^{-1}< {\\rm Tr}\\,\\Phi(0)^{\\dagger} \\Phi(x)>$, where $\\Phi(x)\\sim Z^{-1/2}U(x)$ is the scaling field and $U(x)\\in SU(N)$ is the bare field"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2627","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":""},"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"}