{"paper":{"title":"Equal-charge projection of the $\\mathcal{N}=4$ index: exact large-$N$ formula and finite-rank $U(3)$ coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Miguel Tierz","submitted_at":"2026-07-04T06:44:40Z","abstract_excerpt":"The equal-charge branch of supersymmetric rotating AdS$_5$ black holes has $Q_1=Q_2=Q_3$. The corresponding microcanonical sector of the $\\mathcal{N}=4$ superconformal index is obtained by projecting to equal charges, or equivalently by extracting the constant term in the two charge-difference fugacities. We prove that for the large-$N$ multigraviton sector the projected index factorizes exactly as \\[\n  \\mathcal{I}^{\\rm eqQ}_\\infty(x,p)\n  =\\prod_{k\\ge1}(1-p^kx^{3k})(1-p^{-k}x^{3k})\n  \\sum_{n\\ge0}\\mathsf{p}(n)^3x^{6n}, \\] where $\\mathsf{p}(n)$ is the partition function. This factorization gives"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03735","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/2607.03735/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"}