{"paper":{"title":"Trans-series from condensates in the non-linear sigma model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The limit of the quartic linear sigma model provides a massless perturbative framework for the non-linear sigma model that reproduces its trans-series from condensates at next-to-leading order in 1/N.","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Marcos Mari\\~no, Yizhuang Liu","submitted_at":"2025-07-03T13:27:25Z","abstract_excerpt":"In this work we provide a massless perturbative framework for the two dimensional non-linear sigma model (NLSM), that allows the computation of the perturbative series attached to the operator condensates in the operator product expansion (OPE). It is based on a limit of the quartic linear sigma model (LSM) and is manifestly $O(N)$ symmetric. We show, at next-to-leading order in the $1/N$ expansion, how this framework reproduces the perturbative contribution to the two-point function, as well as its first exponentially small correction due to the condensate of the Lagrangian operator, in full "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"At next-to-leading order in the 1/N expansion, this framework reproduces the perturbative contribution to the two-point function, as well as its first exponentially small correction due to the condensate of the Lagrangian operator, in full agreement with the exact non-perturbative large N solution.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The physics at the natural UV cutoff in the full LSM decouples from the NLSM in the IR in the weak-coupling limit, allowing the perturbative framework for the LSM at the cutoff scale to connect to the one in the NLSM.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new O(N)-symmetric perturbative framework for the 2D NLSM derived from the LSM limit reproduces the perturbative two-point function and its first exponentially small condensate correction at NLO in 1/N, matching the exact large N solution while identifying the leading renormalon as UV and canceled","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The limit of the quartic linear sigma model provides a massless perturbative framework for the non-linear sigma model that reproduces its trans-series from condensates at next-to-leading order in 1/N.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5a278edf66863b7e8b4cf8e42367bdeb30407d0118bf7fe708364df6921392aa"},"source":{"id":"2507.02605","kind":"arxiv","version":2},"verdict":{"id":"ece95319-291d-46b4-bf46-4e926c6c1824","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T06:33:44.237645Z","strongest_claim":"At next-to-leading order in the 1/N expansion, this framework reproduces the perturbative contribution to the two-point function, as well as its first exponentially small correction due to the condensate of the Lagrangian operator, in full agreement with the exact non-perturbative large N solution.","one_line_summary":"A new O(N)-symmetric perturbative framework for the 2D NLSM derived from the LSM limit reproduces the perturbative two-point function and its first exponentially small condensate correction at NLO in 1/N, matching the exact large N solution while identifying the leading renormalon as UV and canceled","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The physics at the natural UV cutoff in the full LSM decouples from the NLSM in the IR in the weak-coupling limit, allowing the perturbative framework for the LSM at the cutoff scale to connect to the one in the NLSM.","pith_extraction_headline":"The limit of the quartic linear sigma model provides a massless perturbative framework for the non-linear sigma model that reproduces its trans-series from condensates at next-to-leading order in 1/N."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.02605/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":47,"sample":[{"doi":"","year":1975,"title":"A. M. Polyakov, Interaction of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields , Phys. Lett. 59B (1975) 79–81","work_id":"bf246277-888a-4919-98f6-e158a1e7a293","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1976,"title":"E. Brezin and J. Zinn-Justin, Spontaneous Breakdown of Continuous Symmetries Near Two-Dimensions, Phys. Rev. B14 (1976) 3110","work_id":"c421defa-d7ce-4390-92c5-cfaa83f6d6fa","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1979,"title":"Parisi, On Infrared Divergences, Nucl","work_id":"48489ad9-f1e4-4d73-a28b-cf8e6a187e8d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"M. Beneke, Renormalons, Phys. Rept. 317 (1999) 1–142, [ hep-ph/9807443]","work_id":"a74edc3e-379c-4cdb-9b63-eb7190f3c218","ref_index":4,"cited_arxiv_id":"hep-ph/9807443","is_internal_anchor":true},{"doi":"","year":1979,"title":"M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, QCD and Resonance Physics. Theoretical Foundations, Nucl. Phys. B 147 (1979) 385–447","work_id":"8b6fab01-3d4f-478a-a18d-86cb1a19acea","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":47,"snapshot_sha256":"97eb93fafca08c5db2e6b762941821201d83f691d90a2fb2ad8cedf261b2005f","internal_anchors":13},"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"}