{"paper":{"title":"Complex Geodesics in the Nariai Geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The two-point correlation function in Nariai geometry equals a sum over complex geodesics obtained by analytic continuation from a sphere product, with phases retained to eliminate spurious singularities.","cross_cats":[],"primary_cat":"hep-th","authors_text":"Lars Aalsma, Mir Mehedi Faruk","submitted_at":"2026-04-29T13:25:49Z","abstract_excerpt":"We study two-point correlation functions of heavy scalar fields in the Nariai geometry. Utilizing the heat kernel formalism, we obtain this result from a geodesic approximation to the two-point function on a product of spheres. By analytically continuing one of the spheres, we obtain the correlation function in the Nariai geometry. This result involves a sum over complex geodesics, extending previous results in pure de Sitter space. We emphasize the important role of the phase of each geodesic contribution, which needs to be taken into account to avoid spurious singularities in the correlator."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The two-point correlation function in the Nariai geometry is given by a sum over complex geodesics obtained via analytic continuation from the sphere product, where the phase of each geodesic contribution must be retained to avoid spurious singularities.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The geodesic approximation to the two-point function remains valid under analytic continuation from the product of spheres to the Nariai geometry, and the heat kernel formalism accurately captures the heavy-field limit without additional corrections.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Obtains the two-point correlator in Nariai geometry as a sum over complex geodesics via heat kernel approximation on sphere products followed by analytic continuation, extending de Sitter results.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The two-point correlation function in Nariai geometry equals a sum over complex geodesics obtained by analytic continuation from a sphere product, with phases retained to eliminate spurious singularities.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"764ee134eef7f54ed77bae4bacb40cf8d4c144df74c935779f04eff94c97ee48"},"source":{"id":"2604.26662","kind":"arxiv","version":2},"verdict":{"id":"46109a70-0e60-45d4-b884-8acc9aa9cf42","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:26:49.344626Z","strongest_claim":"The two-point correlation function in the Nariai geometry is given by a sum over complex geodesics obtained via analytic continuation from the sphere product, where the phase of each geodesic contribution must be retained to avoid spurious singularities.","one_line_summary":"Obtains the two-point correlator in Nariai geometry as a sum over complex geodesics via heat kernel approximation on sphere products followed by analytic continuation, extending de Sitter results.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The geodesic approximation to the two-point function remains valid under analytic continuation from the product of spheres to the Nariai geometry, and the heat kernel formalism accurately captures the heavy-field limit without additional corrections.","pith_extraction_headline":"The two-point correlation function in Nariai geometry equals a sum over complex geodesics obtained by analytic continuation from a sphere product, with phases retained to eliminate spurious singularities."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26662/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T19:56:39.804286Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"402f881f33e56cd63a19d8eeeca6a0f3f2ff67af61276b8efeca15b4e6da590d"},"references":{"count":26,"sample":[{"doi":"","year":2004,"title":"The Black Hole Singularity in AdS/CFT","work_id":"b3939fbf-cb1e-45ee-bbe2-e3821bf4b406","ref_index":1,"cited_arxiv_id":"hep-th/0306170","is_internal_anchor":true},{"doi":"","year":2005,"title":"On charged black holes in anti-de Sitter space","work_id":"ac207a8a-2592-4d67-a23d-160c11f0abe9","ref_index":2,"cited_arxiv_id":"hep-th/0410214","is_internal_anchor":true},{"doi":"","year":2006,"title":"Excursions beyond the horizon: Black hole singularities in Yang-Mills theories (I)","work_id":"c3156f56-5cdc-4457-b35e-d01ecc5a239f","ref_index":3,"cited_arxiv_id":"hep-th/0506202","is_internal_anchor":true},{"doi":"","year":2024,"title":"Black hole singularity from OPE","work_id":"d18b52e7-63d3-445a-95cb-ef28a7108c69","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Imprint of the black hole singularity on thermal two-point functions","work_id":"ceacd7ba-afb9-4433-9667-038b5acaa6c6","ref_index":5,"cited_arxiv_id":"2510.21673","is_internal_anchor":true}],"resolved_work":26,"snapshot_sha256":"29cb48a595be61d90208ba5b72c7fad535c533d73734d9a8fac7a8e882e94ba4","internal_anchors":8},"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"}