The higher derivative regularization and quantum corrections in $\mathcal{N}=2$ supersymmetric theories

Abstract

We construct a new version of the higher covariant derivative regularization for a general $\mathcal{N}=2$ supersymmetric gauge theory formulated in terms of $\mathcal{N}=1$ superfields. This regularization preserves both supersymmetries of the classical action, namely, the invariance under the manifest $\mathcal{N}=1$ supersymmetry and under the second hidden on-shell supersymmetry. The regularizing $\mathcal{N}=2$ supersymmetric higher derivative term is found in the explicit form in terms of $\mathcal{N}=1$ superfields. Thus, $\mathcal{N}=2$ supersymmetry is broken only by the gauge fixing procedure. Then we analyze the exact NSVZ $\beta$-function and prove that in the considered model its higher loop structure is determined by the anomalous dimension of the chiral superfield $\Phi$ in the adjoint representation which is the $\mathcal{N}=2$ superpartner of the gauge superfield $V$. Using the background field method we find that this anomalous dimension is related with the anomalous dimension of the hypermultiplet and vanishes if the effective action is invariant under $\mathcal{N}=2$ background supersymmetry. As a consequence, in this case the higher loop contributions to $\beta$-function also vanish. The one-loop renormalization structure in the considered regularization is also studied by the explicit calculations of the one-loop renormalization constants.

26 pages, 4 figures; the version accepted for publication in Nucl. Phys. B

References in corpus (21)

• Scheme dependence and the NSVZ $\beta$-function
• $N=1$ supersymmetry and the three loop gauge beta function
• The Background Field Method for N = 2 Super Yang-Mills Theories in Harmonic Superspace
• 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
• 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
• Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors
• Calculation of two-loop beta-function for general N=1 supersymmetric Yang--Mills theory with the higher covariant derivative regularization
• The beta function of N=1 SYM in Differential Renormalization
• Two-loop renormalization of N=1 supersymmetric electrodynamics, 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
• Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules
• Universal invariant renormalization of supersymmetric Yang-Mills theory
• Vanishing of the four-loop charge renormalization function in N=4 SYM theory
• Summation of diagrams in N=1 supersymmetric electrodynamics, regularized by higher derivatives
• Operator Product Expansion and Calculation of the Two-Loop Gell-Mann-Low Function
• Multiloop calculations in supersymmetric theories with the higher covariant derivative regularization
• Factorization of integrals, defining the beta-function, into integrals of total derivatives in N=1 SQED, regularized by higher derivatives

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• 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
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• Derivation of the exact expression for the D function in N=1 SQCD
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• 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
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• 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
• Supergraph analysis of the one-loop divergences in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ gauge theories
• 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
• The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings
• The NSVZ $\beta$-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities
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• The higher covariant derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• The three-loop anomalous dimension and the four-loop $\beta$-function for $\mathcal{N}=1$ SQED regularized by higher derivatives
• Hamiltonian Formalism in the Presence of Higher Derivatives
• 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
• The $\beta$-function of supersymmetric theories from vacuum supergraphs: a three-loop example
• Factorization of integrals, defining the beta-function, into integrals of total derivatives in N=1 SQED, regularized by higher derivatives
• On the two-loop divergences in 6D, $\mathcal{N}=(1,1)$ SYM theory
• Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace