Abstract
We argue that for any single-trace operator in \( \mathcal{N} \) = 4 SYM theory there is a large twist double-scaling limit in which the Feynman graphs have an iterative structure. Such structure can be recast using a graph-building operator. Generically, this operator mixes between single trace operators with different scaling limits. The mixing captures both the finite coupling spectrum and corrections away from the large twist limit. We first consider a class of short operators with gluons and fermions for which such mixing problems do not arise, and derive their finite coupling spectra. We then focus on a class of long operators with gluons that do mix. We invert their graph-building operator and prove its integrability. The picture that emerges from this work opens the door to a systematic expansion of \( \mathcal{N} \) = 4 SYM theory around the large twist limit.
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Acknowledgments
We thank S. Chester and D.-l. Zhong for invaluable discussions. We thank D.-l. Zhong for comments on the draft. AS, GF and EU are supported by the Israel Science Foundation (grant number 1197/20). GF is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship.
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Ferrando, G., Sever, A., Sharon, A. et al. A large twist limit for any operator. J. High Energ. Phys. 2023, 28 (2023). https://doi.org/10.1007/JHEP06(2023)028
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DOI: https://doi.org/10.1007/JHEP06(2023)028