{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"aaaa2baeb8401109b1afbe5d38e04b067a5f994b79340da91bda80ec822e7d39","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"386f3cbb2be0a173a004e20472d323c82cd326fa1ea9a830f1df48d9dbacc72d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.swampland.sharpened-distance","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"When a parameter of string theory is moved through a distance $D$, a tower of particles becomes lighter by a factor $\\exp(-\\lambda D)$. The conjecture is that $\\lambda$ can never be smaller than a fixed number set only by the number of spacetime dimensions.","posed_since":"2006","precise":"Distance conjecture (Ooguri and Vafa 2006): along a geodesic of length D in moduli space, measured in Planck units, a tower of states has masses $m \\sim \\exp(-\\lambda D)$. Sharpened version (Etheredge, Heidenreich, Kaya, Qiu, Rudelius 2022): the lightest tower obeys $\\lambda \\ge 1/\\sqrt{d-2}$ in d spacetime dimensions. Prove the bound for all infinite-distance limits of string compactifications, or find a limit with $\\lambda < 1/\\sqrt{d-2}$.","problem_ref":null,"references":"","settled_by":"A proof over all infinite-distance limits of string compactifications in each $d$, or an explicit limit with $\\lambda < 1/\\sqrt{d-2}$.","status_note":"Proposed in 2022 with the bound preserved under dimensional reduction and saturated in many string and M-theory compactifications.","title":"Sharp lower bound on the exponent in the distance conjecture","topic_ref":"21e6e3902bf52f5b90dc25819641c982c2ad6ab4e9dc1db2ec22e07322a801f0"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"6a6212746cc43e9f757ad72a5421ac9b93dfea45504f276de4769686a9265d46","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"78a7b10d6df30ebe77dc653907a942cbbbcf490b619fce82b1ee96f9ce8d2186","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"I-c4UqSaG46LPjiADyJoIrhf3zuYQAhCenWY4Y0WBLWHhaghw43VhSjaCR_Jk-IIg8-KvoJGp8lAocvO53ftCw"},"schema":"pubphys.envelope/1"},"record_hash":"6a6212746cc43e9f757ad72a5421ac9b93dfea45504f276de4769686a9265d46","leaf_index":1963}