The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings

Abstract

We investigate the NSVZ relations for $\mathcal{N}=1$ supersymmetric gauge theories with multiple gauge couplings. As examples, we consider MSSM and the flipped $SU(5)$ model, for which they easily reproduce the results for the two-loop $\beta$-functions. For $\mathcal{N}=1$ SQCD interacting with the Abelian gauge superfield we demonstrate that the NSVZ-like equation for the Adler $D$-function follows from the NSVZ relations. Also we derive all-loop equations describing how the NSVZ equations for theories with multiple gauge couplings change under finite renormalizations. They allow describing a continuous set of NSVZ schemes in which the exact NSVZ $\beta$-functions are valid for all gauge coupling constants. Very likely, this class includes the HD+MSL scheme, which is obtained if a theory is regularized by Higher covariant Derivatives and divergences are removed by Minimal Subtractions of Logarithms. That is why we also discuss how one can construct the higher derivative regularization for theories with multiple gauge couplings. Presumably, this regularization allows to derive the NSVZ equations for such theories in all loops. In this paper we make the first step of this derivation, namely, the NSVZ equations for theories with multiple gauge couplings are rewritten in a new form which relates the $\beta$-functions to the anomalous dimensions of the quantum gauge superfields, of the Faddeev--Popov ghosts, and of the matter superfields. The equivalence of this new form to the original NSVZ relations follows from the extension of the non-renormalization theorem for the triple gauge-ghost vertices, which is also derived in this paper.

arXiv comment39 pages

References in corpus (57)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Two-Loop Renormalization Group Equations for Soft Supersymmetry-Breaking Couplings
• Scheme dependence and the NSVZ $\beta$-function
• $N=1$ supersymmetry and the three loop gauge beta function
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• 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
• Little Miracles of Supersymmetric Evolution of Gauge Couplings
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• On the D = 4, N = 2 Non-Renormalization Theorem
• 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
• Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants
• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• 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
• Calculation of two-loop beta-function for general N=1 supersymmetric Yang--Mills theory with the higher covariant derivative regularization
• Snowmass Benchmark Points and Three-Loop Running
• 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
• The all-loop perturbative derivation of the NSVZ $\beta$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions
• Unification predictions
• One-loop polarization operator of the quantum gauge superfield for $\mathcal{N}=1$ SYM regularized by higher derivatives
• New form of the exact NSVZ $\beta$-function: the three-loop verification for terms containing Yukawa couplings
• A class of the NSVZ renormalization schemes for $\mathcal{N}=1$ SQED
• 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
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• Reduction of Couplings and its application in Particle Physics
• Two-loop renormalization of the matter superfields and finiteness of $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• Factorization of integrals defining the two-loop beta-function for the general renormalizable N=1 SYM theory, regularized by the higher covariant derivatives, into integrals of double total derivatives
• 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
• Exact renormalization of the photino mass in softly broken $\mathcal{N}=1$ SQED with $N_f$ flavors regularized by higher derivatives
• Two-loop renormalization of the Faddeev--Popov ghosts in $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• Reduction of Couplings in the MSSM
• String thresholds and Renormalisation Group Evolution
• The NSVZ $\beta$-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• Two-loop beta-functions and their effects for the R-parity Violating MSSM
• 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
• Multiple Couplings and Renormalization Scheme Ambiguities

Cited by in corpus (6)

• 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 triple gauge-ghost vertices in $\mathcal{N}=1$ supersymmetric gauge theories: the two-loop verification
• 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
• Asymptotic safety guaranteed for strongly coupled gauge theories