{"paper":{"title":"Notes on index of quantum integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bin Chen, Jia Tian, Jue Hou","submitted_at":"2020-02-12T12:36:40Z","abstract_excerpt":"A quantum integrability index was proposed in \\cite{KMS}. It systematizes the Goldschmidt and Witten's operator counting argument \\cite{GW} by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models ${SU(N)}/{SO(N)}$ and $SO(2N)/{SO(N)\\times SO(N)}$. The indexes of these theories are all non-positive except for the case of ${SO(4)}/{SO(2)\\times SO(2)}$. Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the $\\mathbb{CP}^N$ model coupled with a massless Dirac fermion. We find that the index"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.04952","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.04952/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"}