{"paper":{"title":"$\\eta$ invariant of massive Wilson Dirac operator and the index","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.KT"],"primary_cat":"hep-lat","authors_text":"Hidenori Fukaya, Mikio Furuta, Satoshi Yamaguchi, Shinichiroh Matsuo, Shoto Aoki, Tetsuya Onogi","submitted_at":"2025-01-06T09:30:14Z","abstract_excerpt":"We revisit the lattice index theorem in the perspective of $K$-theory. The standard definition given by the overlap Dirac operator equals to the $\\eta$ invariant of the Wilson Dirac operator with a negative mass. This equality is not coincidental but reflects a mathematically profound significance known as the suspension isomorphism of $K$-groups. Specifically, we identify the Wilson Dirac operator as an element of the $K^1$ group, which is characterized by the $\\eta$-invariant. Furthermore, we prove that, at sufficiently small but finite lattice spacings, this $\\eta$-invariant equals to the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02873","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/2501.02873/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"}