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arXiv · 1711.03899

New form of the NSVZ relation at the two-loop level

V. Yu. Shakhmanov·K. V. Stepanyantz
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Abstract

Recently the exact NSVZ $β$-function was rewritten in the form of a relation between the $β$-function and the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields. It was also suggested that this form of the NSVZ equation follows from an underlying equation relating two-point Green functions of the theory. Here we demonstrate that this relation is satisfied at the two-loop level for the non-Abelian ${\cal N}=1$ supersymmetric gauge theories in the case of using the simplest (BRST non-invariant) version of the higher covariant derivative regularization. Consequently, the integrals giving the two-loop $β$-function can be reduced to the one-loop integrals giving the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields.

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V. Yu. Shakhmanov, K. V. Stepanyantz. 2017-12-04. New form of the NSVZ relation at the two-loop level. https://doi.org/10.1016/j.physletb.2017.12.005

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