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 (4)

• 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
• 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
• Vanishing of the four-loop charge renormalization function in N=4 SYM theory

Cited by in corpus (9)

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• The NSVZ beta-function in supersymmetric theories with different regularizations and renormalization prescriptions
• The NSVZ beta-function and the Schwinger-Dyson equations for N=1 SQED with N_f flavors, regularized by higher derivatives
• 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
• NSVZ-like scheme for the photino mass in softly broken $\mathcal{N}=1$ SQED regularized by higher derivatives
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• Hamiltonian Formalism in the Presence of Higher Derivatives