On-shell renormalization scheme for $\mathcal{N}=1$ SQED and the NSVZ relation

Abstract

In this paper we investigate the renormalization of $\mathcal{N}=1$ supersymmetric quantum electrodynamics, regularized by higher derivatives, in the on-shell scheme. It is demonstrated that in this scheme the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) equation relating the $\beta$-function to the anomalous dimension of the matter superfields is valid in all orders of the perturbation theory. This implies that the on-shell scheme enters the recently constructed continuous set of NSVZ subtraction schemes. To verify this statement, we compare the anomalous dimension of the matter superfields in the two-loop approximation and the $\beta$-function in the three-loop approximation, which are explicitly calculated in this scheme. The finite renormalizations relating the on-shell scheme to some other NSVZ subtraction schemes formulated previously are obtained.

18 pages, 1 figure

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Cited by in corpus (6)

• The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings
• Three-loop contribution of the Faddeev-Popov ghosts to the $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories and the NSVZ relation
• Three-loop verification of a new algorithm for the calculation of a $\beta$-function in supersymmetric theories regularized by higher derivatives for the case of $\mathcal{N}=1$ SQED
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• Three-loop $\beta$-functions and two-loop anomalous dimensions for MSSM regularized by higher covariant derivatives in an arbitrary supersymmetric subtraction scheme
• Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace