Nonrenormalization theorems in $N = 1$ supersymmetric gauge theories

Quantum properties of $N=1$ supersymmetric gauge theories regularized by higher covariant derivatives are investigated. Namely, the exact relations between the renormalization group functions in these theories are verified using explicit perturbative calculations. In particular, we perform the two-loop verification of the nonrenormalization theorem for the triple gauge-ghost vertices and the three-loop verification of the new form of the $NSVZ$ relation following from this theorem. To obtain the $\beta$-function, a recently proposed method based on the calculation of modified vacuum supergraphs is used.
The talk is in Russian.