The all-loop perturbative derivation of the NSVZ $\beta$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions

Abstract

The perturbative all-loop derivation of the NSVZ $\beta$-function for $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives is finalized by calculating the sum of singularities produced by quantum superfields. These singularities originate from integrals of double total derivatives and determine all contributions to the $\beta$-function starting from the two-loop approximation. Their sum is expressed in terms of the anomalous dimensions of the quantum gauge superfield, of the Faddeev--Popov ghosts, and of the matter superfields. This allows obtaining the NSVZ equation in the form of a relation between the $\beta$-function and these anomalous dimensions for the renormalization group functions defined in terms of the bare couplings. It holds for an arbitrary renormalization prescription supplementing the higher covariant derivative regularization. For the renormalization group functions defined in terms of the renormalized couplings we prove that in all loops one of the NSVZ schemes is given by the HD+MSL prescription.

arXiv comment42 pages, 5 figures, the version accepted for publication in the European Physical Journal C

References in corpus (53)

• Scheme dependence and the NSVZ $\beta$-function
• $N=1$ supersymmetry and the three loop gauge beta function
• The anomalous dimension of the composite operator A^2 in the Landau gauge
• The Gaugino β-Function
• Exact Results for Soft Supersymmetry Breaking Parameters in Supersymmetric Gauge Theories
• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• On the D = 4, N = 2 Non-Renormalization Theorem
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• The connection between the DRED and NSVZ renormalisation schemes
• Three-loop $\beta$-function for N=1 supersymmetric electrodynamics, regularized by higher derivatives
• Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams
• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants
• Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors
• Lagrange Multipliers and Couplings in Supersymmetric Field Theory
• Precision Calculations in Supersymmetric Theories
• Non-renormalization of the $V\bar{c}c$-vertices in $\mathcal{N}=1$ supersymmetric theories
• Exact Adler Function in Supersymmetric QCD
• One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization
• Manifestly N=2 supersymmetric regularization for N=2 supersymmetric field theories
• The higher derivative regularization and quantum corrections in $\mathcal{N}=2$ supersymmetric theories
• Three-loop NSVZ relation for terms quartic in the Yukawa couplings with the higher covariant derivative regularization
• The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives
• 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
• On the higher-derivative supersymmetric gauge theory
• 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
• A class of the NSVZ renormalization schemes for $\mathcal{N}=1$ SQED
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• 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
• 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
• Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge
• Investigation of the anomaly puzzle in N=1 supersymmetric electrodynamics
• 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 higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories
• On the effective potential in higher-derivative superfield theories
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• Gauge dependence and multiplicative renormalization of Yang-Mills theory with matter fields
• On the effective superpotential in the generic higher-derivative three-dimensional scalar superfield theory
• On the one-loop effective potential in the higher-derivative four-dimensional chiral superfield theory with a nonconventional kinetic term
• One-loop effective potential in the non-local supersymmetric gauge theory
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• On the one-loop effective potential in nonlocal supersymmetric theories
• Horava-Lifshitz four-fermion model revisited and dynamical symmetry breaking

Cited by in corpus (13)

• The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings
• 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
• Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• Exact $\beta$-functions for $\mathcal{N}=1$ supersymmetric theories finite in the lowest loops
• Finiteness of the triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories: the two-loop verification
• Peculiarities of beta functions in sigma models
• The four-loop $\beta$-function from vacuum supergraphs and the NSVZ relation for $\mathcal{N}=1$ SQED regularized by higher derivatives
• The $\beta$-function of supersymmetric theories from vacuum supergraphs: a three-loop example
• Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace
• A condition for the reduction of couplings in the $P=\frac{1}{3}Q$ supersymmetric theories
• Two-loop effective potential for general higher-derivative superfield models
• Asymptotic safety guaranteed for strongly coupled gauge theories