{"paper":{"title":"A Tale of Two Hartle-Hawking Wave Functions: Fully Gravitational vs Partially Frozen","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The phase in Hartle-Hawking wave functions arises only when the gravitational path integral fully integrates over boundary configurations rather than fixing them.","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Galit Anikeeva, Mengyang Zhang, Rapha\\\"el Dulac, Zixia Wei","submitted_at":"2026-05-13T18:00:07Z","abstract_excerpt":"We revisit the Hartle-Hawking wave function in AdS spacetime, where natural spatial slices are open and require an additional spacetime boundary. This leads to two constructions: a fully gravitational wave function, in which the boundary configuration is integrated over, and a partially frozen one, in which it is fixed, as in AdS/CFT. To illustrate the fully gravitational construction, we explicitly analyze it in AdS$_3$ Einstein gravity and AdS$_2$ Jackiw-Teitelboim gravity. We then evaluate the one-loop correction to the hyperbolic-ball partition function in $D$-dimensional AdS Einstein grav"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our results suggest that the phase problem is controlled by whether the gravitational path integral is fully dynamical or partially frozen.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the one-loop correction to the hyperbolic-ball partition function gives the leading contribution to the wave-function norm and that the boundary fluctuations are correctly captured by the chosen regularization.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"In AdS the fully gravitational Hartle-Hawking wave function acquires a nontrivial one-loop phase while the partially frozen version stays real and positive; a partially frozen de Sitter sphere shows phase cancellation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The phase in Hartle-Hawking wave functions arises only when the gravitational path integral fully integrates over boundary configurations rather than fixing them.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bd21580087e6f90d1e5987789d019f17197de9b5bb619a791faf9b0003579998"},"source":{"id":"2605.13970","kind":"arxiv","version":1},"verdict":{"id":"73977e74-ada9-45d0-86ec-c92909cb8c53","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:31:56.341083Z","strongest_claim":"Our results suggest that the phase problem is controlled by whether the gravitational path integral is fully dynamical or partially frozen.","one_line_summary":"In AdS the fully gravitational Hartle-Hawking wave function acquires a nontrivial one-loop phase while the partially frozen version stays real and positive; a partially frozen de Sitter sphere shows phase cancellation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the one-loop correction to the hyperbolic-ball partition function gives the leading contribution to the wave-function norm and that the boundary fluctuations are correctly captured by the chosen regularization.","pith_extraction_headline":"The phase in Hartle-Hawking wave functions arises only when the gravitational path integral fully integrates over boundary configurations rather than fixing them."},"references":{"count":82,"sample":[{"doi":"","year":1983,"title":"J. B. Hartle and S. W. Hawking,Wave Function of the Universe,Phys. Rev. D28 (1983) 2960","work_id":"d1ab83e2-1edb-4867-b7f9-e22b79bcec4b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Review of the no-boundary wave function","work_id":"a49b0469-d8ae-4613-949a-0b3025c5c72d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Maldacena,Comments on the no boundary wavefunction and slow roll inflation, 2403.10510","work_id":"9b985a65-4f4e-471d-98ed-64894d541f20","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"The Large N Limit of Superconformal Field Theories and Supergravity","work_id":"d6d2272a-c223-471a-bbbf-bfe4ee6a8ff3","ref_index":4,"cited_arxiv_id":"hep-th/9711200","is_internal_anchor":true},{"doi":"","year":1998,"title":"Gauge Theory Correlators from Non-Critical String Theory","work_id":"31a4a9b9-435c-4d7b-a180-437bbbabbe5a","ref_index":5,"cited_arxiv_id":"hep-th/9802109","is_internal_anchor":true}],"resolved_work":82,"snapshot_sha256":"83823a34e3f3f70939b489820a979eb827a873956ab23cfbaae57654570c545c","internal_anchors":30},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9030e785c572d3d8e04bcc2807165753ee9f00cfbedcd6da7a6823bc3cfb8586"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}