{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1feadd011a632e287200d59bc6f167cee55593094051cabcb9351139f9e43963","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d3bc35bb02bfc253a422d782fb145ce0144d2edfcfb85dce0565e80c73627801","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qft.massless-bootstrap.photon-bounds","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"At low energy, photons scatter off each other weakly, described by a few numbers. Some combinations of these numbers are bounded by first principles, others appear unconstrained, and the full allowed region is unknown.","posed_since":"","precise":"For the 4D photon effective theory $L = -F^2/4 + a_1 (F_{mn} F^{mn})^2 + a_2 (F_{mn} Ftilde^{mn})^2 + ...$, with no other light states, determine the region of ($a_1$, $a_2$ and higher coefficients, in units of the cutoff) allowed by full nonlinear unitarity, crossing and analyticity, including strongly coupled UV completions, and identify theories on its boundary. Haring, Hebbar, Karateev, Meineri, Penedones (JHEP 10 (2024) 103) obtained numerical bounds and showed that some coefficients cannot be bounded this way.","problem_ref":null,"references":"","settled_by":"Converged numerical bootstrap bounds with an identified family of amplitudes on the boundary.","status_note":"Numerical bounds exist since 2022; the sharp region and the theories at its edge are not established.","title":"Allowed region of four-photon low-energy 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