https://doi.org/10.1140/epjc/s10052-021-09363-7
Regular Article - Theoretical Physics
Exact 
-functions for 
supersymmetric theories finite in the lowest loops
Faculty of Physics, Department of Theoretical Physics, Moscow State University, 119991, Moscow, Russia
Received:
7
May
2021
Accepted:
18
June
2021
Published online:
2
July
2021
We consider a one-loop finite supersymmetric theory in such a renormalization scheme that the first L contributions to the gauge -function and the first 
contributions to the anomalous dimension of the matter superfields and to the Yukawa -function vanish. It is demonstrated that in this case the NSVZ equation and the exact equation for the Yukawa -function in the first nontrivial order are valid for an arbitrary renormalization prescription respecting the above assumption. This implies that under this assumption the 
-loop contribution to the gauge -function and the L-loop contribution to the Yukawa -function are always expressed in terms of the L-loop contribution to the anomalous dimension of the matter superfields. This statement generalizes the result of Grisaru, Milewski, and Zanon that for a theory finite in L loops the -loop contribution to the -function also vanishes. In particular, it gives a simple explanation why their result is valid although the NSVZ equation does not hold in an arbitrary subtraction scheme.
© The Author(s) 2021
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