Abstract
We explore the semi-classical relation between the fuzzy 4-hyperboloid \( {H}_N^4 \) and non-compact quantized twistor space \( {\mathbb{P}}_N^{1,2} \) at large N. This provides two backgrounds of the IKKT matrix model via two natural stereographic projections, leading to higher-spin gauge theories with Euclidean and Minkowski signature denoted by HS-IKKT. The resulting higher-spin gauge theory can be understood as an uplift of \( \mathcal{N} \) = 4 super Yang-Mills to twistor space. The action of HS-IKKT is written using a spinor formalism in both in Euclidean and Minkowski signature. We then compute the tree-level amplitudes of the massless sector within the Yang-Mills part of the HS-IKKT model in the flat limit in Euclidean signature. All n-point tree-level scattering amplitudes for n ≥ 4 of this sector are found to vanish in the flat limit.
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Acknowledgments
We appreciates useful discussions with Zhenya Skvortsov. TT is grateful to Tim Adamo for useful discussion during the collaboration of [39]. This research was partially completed at Corfu Summer Institute 2022 and the Humboldt Kolleg on “Noncommutative and generalized geometry in string theory, gauge theory and related physical models”. The work of TT is partially supported by the Fonds de la Recherche Scientifique under Grants No. F.4503.20 (HighSpinSymm), No. F.4544.21 (Higher- SpinGraWave), and the funding from the European Research Council (ERC) under Grant No. 101002551. The work of HS is supported by the Austrian Science Fund (FWF) grant P32086.
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Steinacker, H.C., Tran, T. Spinorial higher-spin gauge theory from IKKT model in Euclidean and Minkowski signatures. J. High Energ. Phys. 2023, 10 (2023). https://doi.org/10.1007/JHEP12(2023)010
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DOI: https://doi.org/10.1007/JHEP12(2023)010