The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives

Abstract

The effective diagram technique based on the Schwinger-Dyson equations is constructed for N=1 SQED with N_f flavors, regularized by higher derivatives. Using these effective diagrams, it is possible to derive the exact NSVZ relation between the beta-function and the anomalous dimension of the matter superfields exactly in all loops, if the renormalization group functions are defined in terms of the bare coupling constant. In particular, we verify that all integrals which give the beta-function defined in terms of the bare coupling constant are integrals of double total derivatives and prove some identities relating Green functions.

arXiv comment70 pages, 24 figures; v2: a reference added

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• Exact Adler Function in Supersymmetric QCD
• Derivation of the exact expression for the D function in N=1 SQCD
• The all-loop perturbative derivation of the NSVZ $\beta$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions
• New form of the exact NSVZ $\beta$-function: the three-loop verification for terms containing Yukawa couplings
• One-loop polarization operator of the quantum gauge superfield for $\mathcal{N}=1$ SYM regularized by higher derivatives
• Structure of three-loop contributions to the beta-function of N=1 SQED with N_f flavors, regularized by the dimensional reduction
• The $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives as an integral of double total derivatives
• Two-loop renormalization of the matter superfields and finiteness of $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• NSVZ-like scheme for the photino mass in softly broken $\mathcal{N}=1$ SQED regularized by higher derivatives
• Exact renormalization of the photino mass in softly broken $\mathcal{N}=1$ SQED with $N_f$ flavors regularized by higher derivatives
• On-shell renormalization scheme for $\mathcal{N}=1$ SQED and the NSVZ relation
• The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings
• Two-loop renormalization of the Faddeev--Popov ghosts in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• The NSVZ $\beta$-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities
• Three-loop contribution of the Faddeev-Popov ghosts to the $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories and the NSVZ relation
• The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories
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• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• Subtleties in the beta function calculation of N=1 supersymmetric gauge theories
• Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
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• The $\beta$-function of supersymmetric theories from vacuum supergraphs: a three-loop example
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• Non-perturbative SQED beta function using functional renormalization group approach and the NSVZ exact beta function