Abstract
We study four point planar loop amplitudes at an arbitrary point in the Coulomb branch of \( \mathcal{N} \) = 4 super-Yang-Mills theory. We study two particle unitary cuts up to four loop order. We explicitly verify that bubble and triangle graphs do not contribute at one loop level and show that the results hold at higher loop level as well. We also write down an all loop recursion relation for two particle reducible graphs for four point amplitudes.
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Acknowledgments
We thank Sujay K. Ashok, Kushal Chakraborty, Aakash Kumar, Alok Laddha, Suvrat Raju, Arnab Rudra, Bindusar Sahoo, and Ashoke Sen for illuminating discussions. We thank the anonymous referee for helpful comments on the manuscript. MA, SH, and AS thank participants of Student Talks on Trending Topics in Theory (ST4 2023) for enlightening discussions. APS thanks all the members of the string theory group at IISER Bhopal for several useful discussions. DPJ would like to thank McGill University for warm hospitality. MA thanks ICTS, CMI, and IMSc for hospitality. SH thanks IIT Ropar, AEI Potsdam for hospitality. APS thanks IMSc, CMI for hospitality. During the course of this project APS has been supported by SERB National Post-Doctoral Fellowship. MA acknowledges support from the Infosys foundation fellowship grant.
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Abhishek, M., Hegde, S., Jatkar, D.P. et al. Loop amplitudes in the Coulomb branch of \( \mathcal{N} \) = 4 super-Yang-Mills theory. J. High Energ. Phys. 2024, 143 (2024). https://doi.org/10.1007/JHEP03(2024)143
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DOI: https://doi.org/10.1007/JHEP03(2024)143