The NSVZ $\beta$-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities

Abstract

The contributions of the matter superfields and of the Faddeev--Popov ghosts to the $\beta$-function of $\mathcal{N}=1$ supersymmetric gauge theories defined in terms of the bare couplings are calculated in all orders in the case of using the higher covariant derivative regularization. For this purpose we use the recently proved statement that the $\beta$-function in these theories is given by integrals of double total derivatives with respect to the loop momenta. These integrals do not vanish due to singularities of the integrands. This implies that the $\beta$-function beyond the one-loop approximation is given by the sum of the singular contributions, which is calculated in all orders for singularities produced by the matter superfields and by the Faddeev--Popov ghosts. The result is expressed in terms of the anomalous dimensions of these superfields. It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices.

arXiv comment38 pages, 4 figures

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Cited by in corpus (12)

• The all-loop perturbative derivation of the NSVZ $\beta$-function and the NSVZ scheme in the non-Abelian case by summing singular contributions
• Two-loop renormalization of the matter superfields and finiteness of $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher derivatives
• 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
• On supersymmetric gauge theories with higher derivatives and nonlocal terms in the matter sector
• 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 $\beta$-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
• Two-loop effective potential for general higher-derivative superfield models