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In this note we show that $\beta'_*$, the $\beta$-function slopes in theelectric and magnetic theories are equal at the corresponding infrared fixedpoints. This follows from the scaling of the correlators of the trace of theenergy momentum tensors. The slopes $\beta'_*$ determine the scalingdimensions. Our paper can be considered as a commentary to Anselmi et al. [1]-- it proposes an improved derivation not based on a rather contrivedconstruction by Kutasov et al. [2]. As a byproduct we note that $\gamma'_{Q^*}$-- the slopes of the matter superfield anomalous dimension -- vanish at bothedges of the conformal window where one of the dual theories is stronglycoupled. Finally, we determine the two-coupling magnetic fixed point at weakcoupling correcting the result of [3]}.

Relating $\beta'_*$ and $\gamma'_{Q*}$ in the ${\cal N}=1$ SQCD Conformal Window

Relating $\beta'_$ and $\gamma'_{Q}$ in the ${\cal N}=1$ SQCD Conformal Window