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arXiv · 2204.08297

All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron

Song He·Chia-Kai Kuo·Zhenjie Li·Yao-Qi Zhang
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Abstract

We define a new geometry obtained from the all-loop amplituhedron in ${\cal N}=4$ SYM by reducing its four-dimensional external and loop momenta to three dimensions. Focusing on the simplest four-point case, we provide strong evidence that the canonical form of this ``reduced amplituhedron" gives the all-loop integrand of the ABJM four-point amplitude. In addition to various all-loop cuts manifested by the geometry, we present explicitly new results for the integrand up to five loops, which are much simpler than results in ${\cal N}=4$ SYM. One of the reasons for such all-loop simplifications is that only a very small fraction of the so-called negative geometries survive the dimensional reduction, which corresponds to bipartite graphs. Our results suggest an unexpected relation between four-point amplitudes in these two theories.

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Song He, Chia-Kai Kuo, Zhenjie Li, Yao-Qi Zhang. 2023-01-18. All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron. https://doi.org/10.1103/physrevlett.129.221604

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