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arXiv · 1603.04801

Non-renormalization of the $V\bar cc$-vertices in ${\cal N}=1$ supersymmetric theories

K. V. Stepanyantz
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Abstract

Using the Slavnov--Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in ${\cal N}=1$ supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant derivative regularization. Using the restrictions to the renormalization constants which are imposed by the non-renormalization of the considered vertices we express the exact NSVZ $β$-function in terms of the anomalous dimensions of the Faddeev--Popov ghosts and of the quantum gauge superfield. In the expression for the NSVZ $β$-function obtained in this way the contributions of the Faddeev--Popov ghosts and of the matter superfields have the same structure.

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K. V. Stepanyantz. 2018-08-20. Non-renormalization of the $V\bar cc$-vertices in ${\cal N}=1$ supersymmetric theories. https://doi.org/10.1016/j.nuclphysb.2016.05.011

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