Three-loop five-leg amplitude in planar N=4 sYM near mass shell is computed via 6D unitarity cuts and dimensional reduction, confirming IR exponentiation governed by octagon anomalous dimension with each of three kinematic structures having its own function of 't Hooft coupling.
Coronado,Bootstrapping the Simplest Correlator in PlanarN= 4Supersymmetric Yang-Mills Theory to All Loops,Phys
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In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
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.
In the classical strong-coupling regime, half-BPS correlation functions in planar N=4 SYM exponentiate under the hexagon formalism and are governed by TBA equations structurally equivalent to Gaiotto-Moore-Neitzke equations, enabling a chi-system for both polygonal and closed geometries.
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.
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Notes on off-shell conformal integrals and correlation functions at five points
A basis of six uniform-transcendental five-point off-shell conformal integrals is constructed and mapped to known families, yielding symbol-level two-loop results for half-BPS correlators.