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Higher-loop integrated negative geometries in ABJM
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abstract
In the three-dimensional ${\cal N}=6$ Chern-Simons matter (ABJM) theory, the integrand for the logarithm of the scattering amplitude admits a decomposition in terms of negative geometries, which implies that all the infrared divergences concentrate in the last loop integration. We compute the infrared-finite functions that arise from performing a three-loop integration over the four-loop integrand for the logarithm of the four-point amplitude, for which we use the method of differential equations. Our results provide a direct computation of the four-loop cusp anomalous dimension of the theory, in agreement with the current all-loop integrability-based proposal. We find an apparent simplicity in the leading singularities of the integrated results, provided one works in the frame in which the unintegrated loop variable goes to infinity. Finally, our results suggest an alternating sign pattern for the integrated negative geometries in the Euclidean region.
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Two-loop four-point amplitudes on the Coulomb branch of ${\mathcal{N}}=4$ super Yang-Mills
The subleading Regge-limit exponent of a Coulomb branch four-point amplitude in N=4 SYM matches the anomalous dimension of a cusped Wilson loop with a scalar insertion, known from integrability.
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