# Contribution of $\text{SU}(\text{N})$ gauge coupling $\beta$-function of chiral fermions in given representation of $\text{SU}(\text{N})$?

Consider the supersymmetric extension of the Standard Model. For each chiral fermion (left or right) there is a complex scalar, which transforms under the same representation of the gauge group$$\text{SU}(3)_\text{c} \times \text{SU}(2)_\text{L} \times \text{U}(1)_\text{Y}.$$For each gauge boson there is a Majorana fermion (half of degrees of freedom of Dirac fermion) transforming in the adjoint representation of the gauge group. In addition, instead of one there are two Higgs fields, which transform in the fundamental representation of $\text{SU}(2)_\text{L}$, and which have hypercharges equal to $1/2$ and $-1/2$ respectively. For each of the Higgs fields there is a chiral fermion transforming in the same representation of the gauge group as the Higgs fields.

Question. Where is it worked out that the contribution of the $\text{SU}(\text{N})$ gauge coupling $\beta$-function of chiral fermions in a given representation of $\text{SU}(\text{N})$ is equal to$$\beta(\text{g})_{\text{ch.f.}} = -\text{g}^3/(4\pi)^2(-2\text{n}_\text{f}\text{C}(\text{r})/3),$$where $\text{n}_\text{f}$ is the number of chiral fermions in the representation $\text{r}$?

I assume this must be quite well-known/standard, but I don't know where to go to search for this.

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