Abstract
We consider correlation functions of supersymmetrized determinant operators in self-dual super Yang-Mills (SYM). These provide a generating function for correlators of arbitrary single-trace half-BPS operators, including, for appropriate Grassmann components, the so-called loop integrand of the non-self-dual theory. We introduce a novel twistor space representation for determinant operators which makes contact with the recently studied m = 2 amplituhedron. By using matrix duality we rewrite the n-point determinant correlator as a n × n matrix integral where the gauge group rank Nc is turned into a coupling. The correlators are rational functions whose denominators, in the planar limit, contain only ten-dimensional distances. Using this formulation, we verify a recent conjecture regarding the ten-dimensional symmetry of the components with maximal Grassmann degree and we obtain new formulas for correlators of Grassmann degree four.
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Acknowledgments
It is a great pleasure to acknowledge Shota Komatsu and Matteo Parisi for useful discussions. BM is supported in part by the Simons Foundation Grant No. 385602 and the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number SAPIN/00047-2020. Work of SCH and FC are supported in parts by the Simons Collaboration on the Nonperturbative Bootstrap. Work of SCH is also supported by the Simons Fellowships in Theoretical Physics and the Canada Research Chair program funding reference CRC-2021-00421. SCH is grateful for hospitality at the Institute for Advanced Study, where part of this work was carried out.
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Caron-Huot, S., Coronado, F. & Mühlmann, B. Determinants in self-dual \( \mathcal{N} \) = 4 SYM and twistor space. J. High Energ. Phys. 2023, 8 (2023). https://doi.org/10.1007/JHEP08(2023)008
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DOI: https://doi.org/10.1007/JHEP08(2023)008