https://doi.org/10.1140/epjc/s10052-019-7323-1
Regular Article - Theoretical Physics
Three-loop contribution of the Faddeev–Popov ghosts to the 
-function of 
supersymmetric gauge theories and the NSVZ relation
Department of Theoretical Physics, Faculty of Physics, Moscow State University, 119991, Moscow, Russia
* e-mail: stepan@m9com.ru
Received:
3
September
2019
Accepted:
18
September
2019
Published online:
28
September
2019
We find the three-loop contribution to the -function of supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev–Popov ghosts. This is done using a recently proposed algorithm, which essentially simplifies such multiloop calculations. The result is presented in the form of an integral of double total derivatives in the momentum space. The considered contribution to the -function is compared with the two-loop anomalous dimension of the Faddeev–Popov ghosts. This allows verifying the validity of the NSVZ equation written as a relation between the -function and the anomalous dimensions of the quantum superfields. It is demonstrated that in the considered approximation the NSVZ equation is satisfied for the renormalization group functions defined in terms of the bare couplings. The necessity of the nonlinear renormalization for the quantum gauge superfield is also confirmed.
© The Author(s), 2019
