$\mathcal{N}=8$ Supergravity from Positivity

Journal Article · 18 February 2025 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.134.071603 · OSTI ID:2519711

Carrasco, John Joseph M. ; Edison, Alex ; Robles Del Pino, Nia ; Zekioğlu, Suna

The duality between color and kinematics brings many simplifications to the construction of scattering amplitudes. Here, we show that satisfaction of the tree-level Bern-Carrasco-Johansson relations can dramatically simplify loop computations even when the loop-level relations are not explicitly satisfied. We introduce an agglomerative algorithm, color-dual cut tiling, that builds the entire integrand from the simplest on-shell conditions applied to a seed of off-shell integrand information. Specifically, we demonstrate that for two-to-two scattering at three loops in the maximally supersymmetric gauge theory there is sufficient information contained in planar cuts—completely determined by positivity constraints—to generate all of the nonplanar sector. We further make use of the generalized double copy to generate a representation of maximally supersymmetric gravity as a functional of the planar SYM input. We close with comments on generalizations and possible applications of the approach. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0015910
• OSTI ID: 2519711
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 7 Vol. 134; ISSN 0031-9007; ISSN PRLTAO
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English