{"paper":{"title":"The Epsilon Expansion Meets Semiclassics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-ph"],"primary_cat":"hep-th","authors_text":"Alexander Monin, Gabriel Cuomo, Gil Badel, Riccardo Rattazzi","submitted_at":"2019-09-03T16:05:05Z","abstract_excerpt":"We study the scaling dimension $\\Delta_{\\phi^n}$ of the operator $\\phi^n$ where $\\phi$ is the fundamental complex field of the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\\varepsilon$. Even for a perturbatively small fixed point coupling $\\lambda_*$, standard perturbation theory breaks down for sufficiently large $\\lambda_*n$. Treating $\\lambda_* n$ as fixed for small $\\lambda_*$ we show that $\\Delta_{\\phi^n}$ can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in $$ \\Delta_{\\phi^n}=\\frac{1}{\\lambda_*}\\Delta_{-1}(\\lambda_* n)+\\Del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01269","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/1909.01269/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"}