Derivation of the exact expression for the D function in N=1 SQCD

Abstract

We discuss various details of our derivation of the exact expression for the Adler D function in N=1 supersymmetric QCD (SQCD). This exact formula relates the D function to anomalous dimensions of the matter superfields. Our perturbative derivation refers to the D function defined in terms of the bare coupling constant in the case of using the higher covariant derivative regularization. The exact expression for this function is obtained by direct summation of supergraphs to all orders in the non-Abelian coupling constant. As we argued previously, our formula should be valid beyond perturbation theory too. The perturbative result we present here coincides with the general formula order by order. We discuss consequences for N=1 SQCD in the conformal window. It is noted that our exact relation can allow one to determine the (infrared) critical anomalous dimension of the Seiberg M field present in the dual theory.

arXiv comment30 pp, 9 figures; v2. one figure corrected

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• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
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• 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
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• 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
• Three-loop $\beta$-functions and two-loop anomalous dimensions for MSSM regularized by higher covariant derivatives in an arbitrary supersymmetric subtraction scheme
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• Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term
• Infrared Renormalons in Supersymmetric Theories
• Non-Abelian gauge theories with composite fields in the background field method
• Supersymmetric Adler Functions and Holography
• Exact results in explicit three-loop calculations using higher derivatives for $\mathcal{N}=1$ SQCD