{"paper":{"title":"On Certain Spectral Invariants of Dirac Operators on Noncommutative Tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Ali Fathi, Masoud Khalkhali","submitted_at":"2015-04-05T23:53:02Z","abstract_excerpt":"The spectral eta function for certain families of Dirac operators on noncommutative $3$-torus is considered and the regularity at zero is proved. By using variational techniques, we show that $\\eta_{D}(0)$ is a conformal invariant. By studying the Laurent expansion at zero of $\\text{TR} (|D|^{-z})$, the conformal invariance of $\\zeta'_{|D|}(0)$ for noncommutative $3$-torus is proved. Finally, for the coupled Dirac operator, a local formula for the variation $\\partial_A\\eta_{D+A}(0)$ is derived which is the analogue of the so called induced Chern-Simons term in quantum field theory literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01174","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":""},"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"}