Abstract
We elaborate on aspects of a new positive geometry proposed recently, which was conjectured to be the four-point amplituhedron for ABJM theory. We study generalized unitarity cuts from the geometry, and in particular we prove that (1) the four-point integrand satisfies perturbative unitarity (or optical theorem) to all loops, which follows directly from the geometry, and (2) vanishing cuts involving odd-point amplitudes follow from the “bipartite” nature of the associated “negative geometries”, which justifies their appearance in ABJM theory. We also take a first step in integrating the forms of these negative geometries and obtain an infrared-finite quantity up to two loops, from which we extract the cusp anomalous dimension at leading order.
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Acknowledgments
We thank Yu-tin Huang for stimulating discussions and collaborations on related projects. We are grateful to Johaness Henn, Martin Lagares and Shun-Qing Zhang for sharing their results with us. This research is supported in part by National Natural Science Foundation of China under Grant No. 11935013, 12047502, 12047503, 12247103, 12225510. This work is also supported in part by the U.S. Department of Energy under contract number DE-AC02-76SF00515. C.-K. Kuo is supported by Taiwan Ministry of Science and Technology Grant No. 109-2112-M-002-020-MY3, National Science and Technology Council of Taiwan, Grant No. 111-2811-M-002-125, as well as MOST 110-2923-M-002-016-MY3.
Note added. While this work was in progress, we were made aware of an upcoming work [44], where the finite function up to L = 3 has been computed and the two results agree.
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He, S., Kuo, CK., Li, Z. et al. Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron. J. High Energ. Phys. 2023, 212 (2023). https://doi.org/10.1007/JHEP07(2023)212
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DOI: https://doi.org/10.1007/JHEP07(2023)212