One-cycle negative geometries in N=4 SYM have singularities only at z=-1, 0, and infinity to all loop orders.
Arkani-Hamed, J
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ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes encoded in a permutation-symmetric generating function of planar f-graphs.
Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
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Multi-Loop Negative Geometries
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.