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

TL;DR

This paper derives an exact expression for the D function in N=1 SQCD, relating it to anomalous dimensions, using supergraph summation and regularization techniques, with implications for conformal window dynamics.

Contribution

It provides the first exact, all-orders derivation of the D function in N=1 SQCD, connecting it to anomalous dimensions via supergraph summation.

Findings

Exact expression for the D function in N=1 SQCD derived

Perturbative results match the exact formula order by order

Implications for the conformal window and dual theory anomalous dimensions

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.