The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions

Abstract

We briefly review the calculations of quantum corrections related with the exact NSVZ $\beta$-function in $\mathcal{N}=1$ supersymmetric theories, paying especial attention to the scheme dependence of the results. It is explained, how the NSVZ relation is obtained for the renormalization group functions defined in terms of the bare coupling constant if a theory is regularized by higher derivatives. Also we describe, how to construct a special renormalization prescription which gives the NSVZ relation for the renormalization group functions defined in terms of the renormalized coupling constant exactly in all orders for Abelian supersymmetric theories, regularized by higher derivatives. The scheme dependence of the NSVZ $\beta$-function (for the renormalization group functions defined in terms of the renormalized coupling constant) is discussed in the non-Abelian case. It is shown that in this case the NSVZ $\beta$-function leads to a certain scheme-independent equality.

11 pages

References in corpus (6)

• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams
• The higher derivative regularization and quantum corrections in $\mathcal{N}=2$ supersymmetric theories
• The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Vanishing of the four-loop charge renormalization function in N=4 SYM theory

Cited by in corpus (15)

• Exact Adler Function in Supersymmetric QCD
• The NSVZ scheme for $\mathcal{N}=1$ SQED with $N_f$ flavors, regularized by the dimensional reduction, in the three-loop approximation
• Derivation of the exact expression for the D function in N=1 SQCD
• New form of the NSVZ relation at the two-loop level
• One-loop polarization operator of the quantum gauge superfield for $\mathcal{N}=1$ SYM regularized by higher derivatives
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• NSVZ-like scheme for the photino mass in softly broken $\mathcal{N}=1$ SQED regularized by higher derivatives
• On-shell renormalization scheme for $\mathcal{N}=1$ SQED and the NSVZ relation
• 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
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Gauge Coupling Field, Currents, Anomalies and N=1 Super-Yang-Mills Effective Actions