Quantum properties of gauge theories with extended supersymmetry formulated in $\mathcal{N}=1$ superspace

Abstract

We analyse quantum properties of $\mathcal{N}=2$ and $\mathcal{N}=4$ supersymmetric gauge theories formulated in terms of $\mathcal{N}=1$ superfields and investigate the conditions imposed on a renormalization prescription under which the non-renormalization theorems are valid. For this purpose in these models we calculate the two-loop contributions to the anomalous dimensions of all chiral matter superfields and the three-loop contributions to the $\beta$-functions for an arbitrary $\mathcal{N}=1$ supersymmetric subtraction scheme supplementing the higher covariant derivative regularization. We demonstrate that, in general, the results do not vanish due to the scheme dependence, which becomes essential in the considered approximations. However, the two-loop anomalous dimensions vanish if a subtraction scheme is compatible with the structure of quantum corrections and does not break the relation between the Yukawa and gauge couplings which follows from $\mathcal{N}=2$ supersymmetry. Nevertheless, even under these conditions the three-loop contribution to the $\beta$-function does not in general vanishes for $\mathcal{N}=2$ supersymmetric theories. To obtain the purely one-loop $\beta$-function, one should also chose an NSVZ renormalization prescription. The similar statements for the higher loop contributions are proved in all orders.

arXiv comment26 pages

References in corpus (39)

• Scheme dependence and the NSVZ $\beta$-function
• $N=1$ supersymmetry and the three loop gauge beta function
• $N=1$ supersymmetry and the three loop anomalous dimension for the chiral superfield
• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• 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
• 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
• Scheme independent consequence of the NSVZ relation for N=1 SQED with N_f flavors
• Precision Calculations in Supersymmetric Theories
• Non-renormalization of the $V\bar{c}c$-vertices in $\mathcal{N}=1$ supersymmetric theories
• 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
• 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
• Three-loop renormalization of the N=1, N=2, N=4 supersymmetric Yang-Mills theories
• 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
• 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
• On-shell renormalization scheme for $\mathcal{N}=1$ SQED and the NSVZ relation
• The NSVZ relations for $\mathcal{N}=1$ supersymmetric theories with multiple gauge couplings
• 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
• 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
• Three-loop calculations in non-Abelian gauge theories
• Vanishing of the four-loop charge renormalization function in N=4 SYM theory
• 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
• The $\beta$-function of supersymmetric theories from vacuum supergraphs: a three-loop example

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