{"paper":{"title":"One-loop divergences for KK theories on $\\mathrm{AdS}\\times S$ spaces; a reanalysis of $\\mathrm{AdS}_4 \\times S^7$ /ABJM precision holography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Federico Arrighi, Lorenzo Casarin","submitted_at":"2026-05-31T11:18:39Z","abstract_excerpt":"We provide a systematic framework for computing the logarithmically divergent part of one-loop partition functions on product spaces $\\mathrm{AdS}_{d_A} \\times S^{d_S}$ of arbitrary dimension. By expanding the higher-dimensional kinetic operators in spherical harmonics, we reduce the ($d_A+d_S$)-dimensional spectral problem to an infinite tower of $d_A$-dimensional determinants, which are then represented via spectral $\\zeta$-function methods. We isolate the logarithmic divergences arising from the interplay between the individual AdS determinants and the infinite Kaluza-Klein sum, carefully a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01167","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/2606.01167/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"}