{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a87f1bc69b1efb66f85290f54af13fa05363f52934d7670fa12147c7f7a3451b","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"64bd7209b61d63da62aa9700e04e2bab0bef9ccce50f39ba3b96fe854fdfcdbb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qft.massless-bootstrap.graviton-4d","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In ten and eleven dimensions, bootstrap methods have mapped which graviton-scattering amplitudes are allowed and where string theory lies. In four dimensions the same analysis is blocked by infinities from very low-energy gravitons.","posed_since":"","precise":"For $D = 4$ $2\\to 2$ graviton scattering with Newton constant $G$, determine nonperturbatively (without assuming a weakly coupled UV completion) the allowed range of the leading higher-derivative coefficients ($R^{3}$ and $R^{4}$ terms) in units of the cutoff, using full nonlinear unitarity. The $D = 10$ analogue was mapped by Guerrieri, Penedones, Vieira (Phys. Rev. Lett. 127, 081601, 2021); in $D = 4$ the infrared divergences must be handled first.","problem_ref":null,"references":"","settled_by":"A numerical bootstrap in $D = 4$ with a controlled infrared treatment giving converged bounds.","status_note":"","title":"Nonperturbative bounds on four-dimensional graviton scattering","topic_ref":"ec37b6151c82884c89bcd0edd8abd842fda27798c1918aa964b247ee16f12213"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9aa34d7aa46072c0dc2b8ccd18839658c7d79e439f1ff26ea63b4430011a729a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c4904ed6002154aaca64923e4a2e28fb2e96f69cecd4f6e872ab02e588c5654a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"cjSwfTImpai5Ci8ZdKx5STXpTOgogv0Q20HHv6KPRX26hwliNJJ6mg7Ztu7Gb0Ml8SE4AZ4_O-dsmICEe_dQCw"},"schema":"pubphys.envelope/1"},"record_hash":"9aa34d7aa46072c0dc2b8ccd18839658c7d79e439f1ff26ea63b4430011a729a","leaf_index":1922}