Abstract
We investigate the NSVZ equation in \(\mathcal{N} = 1\) supersymmetric gauge theories, which relates the \(\beta \)‑function to the anomalous dimension of the matter superfields. In particular, we argue that it is closely connected with the non-renormalization theorem for the three-point gauge-ghost vertices (in which one external leg corresponds to the quantum gauge superfield). Using finiteness of these vertices the exact NSVZ \(\beta \)-function can be equivalently presented in the form of a relation between the \(\beta \)-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev–Popov ghosts, and of the matter superfields. This equation allows explaining how the NSVZ equation appears in the perturbation theory for theories regularized by higher covariant derivatives and constructing the NSVZ scheme in all orders in the case of using this regularization. The results are verified by an explicit three-loop calculation of the terms quartic in the Yukawa couplings.
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Stepanyantz, K.V. NSVZ Relation in Supersymmetric Theories Regularized by Higher Derivatives. Phys. Part. Nuclei 49, 908–910 (2018). https://doi.org/10.1134/S1063779618050374
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DOI: https://doi.org/10.1134/S1063779618050374