Abstract
We study the mixing of operators under renormalization group flow in quantum theories, and prove a non-renormalization theorem at non-linear order. It dictates zeros up to a certain number of loops in anomalous dimension tensors that control, for example, the mixing of operators at order dimension six squared into dimension eight. We obtain new results at up to three loops for the mass dimension eight anomalous dimension tensor of ϕ4 theory in D = 4 − 2ε dimensions and verify the zeros predicted by the theorem.
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Acknowledgments
We thank J. Vermaseren for providing us with a private version of FORM which includes an interface to the graph generator by T. Kaneko. J.R.N. is grateful to the DESY Hamburg Theory group for hospitality.
W.C. is also supported by the Global Science Graduate Course (GSGC) program of the University of Tokyo, and acknowledges support from JSPS KAKENHI Grants No. 19H05810 and No. 22J21553. F.H. is supported by the NWO Vidi grant 680-47-551 and the UKRI FLF Mr/S03479x/1. T.M. is supported by the World Premier International Research Center Initiative (WPI) MEXT, Japan, and by JSPS KAKENHI grants JP19H05810, JP20H01896, JP20H00153, and JP22K18712. J.R.N. is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Projektnummer 417533893/GRK2575 “Rethinking Quantum Field Theory”.
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Cao, W., Herzog, F., Melia, T. et al. Non-linear non-renormalization theorems. J. High Energ. Phys. 2023, 80 (2023). https://doi.org/10.1007/JHEP08(2023)080
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DOI: https://doi.org/10.1007/JHEP08(2023)080