{"paper":{"title":"One-loop supergravity on $\\mathrm{AdS}_4\\times S^7/\\mathbb{Z}_k$ and comparison with ABJM theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"James T. Liu, Wenli Zhao","submitted_at":"2016-09-08T20:00:01Z","abstract_excerpt":"The large-$N$ limit of ABJM theory is holographically dual to M-theory on AdS$_4\\times S^7/\\mathbb{Z}_k$. The 3-sphere partition function has been obtained via localization, and its leading behavior $F_{\\text{ABJM}}^{(0)}\\sim k^{1/2}N^{3/2}$ is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading $\\mathcal O(N^0)$ order by computing the one-loop supergravity free energy as a function of $k$ and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with $F_{\\text{SUGRA}}^{(1)}\\sim k^6$, while $F_{\\text{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02558","kind":"arxiv","version":3},"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"}